Phd Thesis: Numerical modelling of surface subsidence associated with block caving mining using...

NUMERICAL MODELLING OF SURFACE SUBSIDENCE

ASSOCIATED WITH BLOCK CAVE MINING USING A FINITE ELEMENT / DISCRETE ELEMENT APPROACH

by

Alexander Vyazmensky

Master of Applied Science, University of British Columbia, 2005

THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

In the Earth Sciences

© Alexander Vyazmensky 2008

SIMON FRASER UNIVERSITY

Fall 2008

All rights reserved. This work may not be reproduced in whole or in part, by photocopy

or other means, without permission of the author.

http://sites.google.com/site/alexvyazmensky/

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ABSTRACT

Recent years have seen a major increase of interest in the block cave mining

method which is characterized by extraction of a massive volume of rock usually

accompanied by the formation of a significant surface depression above and in the

vicinity of the mining operation. The ability to predict surface subsidence is

important for mine planning, operational hazard assessment and evaluation of

environmental and socio-economic impacts. Owing to problems of scale and lack

of access, the fundamental understanding of the complex rock mass response

leading to subsidence is limited as are current subsidence prediction capabilities.

Through the use of an integrated FEM/DEM-DFN modelling technique this thesis

presents a new approach to simulation of block caving induced surface

subsidence allowing physically realistic simulation of subsidence development

from caving initiation to final subsidence deformation. As part of the current

research, a fundamental issue in modelling, the selection of representative

equivalent continuum rock mass modelling parameters, is investigated and a

procedure for calibration of modelling parameters devised. Utilizing a series of

conceptual numerical experiments our fundamental understanding of the

mechanisms and the role of the factors controlling block caving subsidence

development is investigated. Valuable insights gained from this work are

summarized in a preliminary subsidence classification and an influence

assessment matrix of the governing factors. These are intended as an aid to

engineering judgment for decision makers at the pre-feasibility and mine design

stages.

This study also addresses one of the most challenging problems in mining rock

engineering - the interaction between block cave mining and a large overlying

open pit, focusing on caving induced step-path failure initialization. Using a novel

approach to modelling data analysis a clear link between caving propagation, step-


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path failure development within the slope, and the resultant surface subsidence is

established. In addition, FEM/DEM-DFN modelling is applied to the preliminary

analysis of the block caving triggered slope failure at Palabora open pit.

This research represents a valuable contribution to block caving geomechanics

and is a major step forward in the understanding of complex block caving

subsidence phenomena, paving the way to more reliable assessment of caving

induced subsidence deformations.

Keywords: rock mechanics; numerical modelling; block cave mining; block

caving subsidence; open pit - caving mining interaction; FEM/DEM-DFN


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DEDICATION

I dedicate this work to my parents, Mikhail and Sofia, who offered unconditional

love and support and have always been there for me. Thank you so much.


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ACKNOWLEDGEMENTS

It is my pleasure to acknowledge the roles of several individuals who were

instrumental for completion of my Ph.D. research.

First of all, I would like to express my gratitude to Dr. Doug Stead, who encouraged

me to pursue this project and taught me the art of rock engineering. I truly enjoyed

working in a research environment that stimulates original thinking and initiative,

which he created. Dr. Stead‟s skilful guidance, innovative ideas and stoic patience

are greatly appreciated.

I would like to acknowledge the valuable input of Dr. Davide Elmo, who contributed

to many discussions that helped to shape this project, assisted with FracMan and

was always willing to help resolving the most difficult modelling issues.

I would also like to acknowledge helpful suggestions from my committee members:

Dr. Erik Eberhardt, Dr. Scott Dunbar, Dr. Malcolm Scoble and Dr. Diana Allen.

This work would not materialize without the financial support of Rio Tinto Pty and

technical support by Rockfield Technology Ltd and Golder Associates Ltd. I would

like to recognize the important roles of Allan Moss, Andre van As, Dr. Jon Rance,

Dr. Melanie Armstrong and Dr. Steve Rogers.

These acknowledgements would not be complete without mentioning my research

lab colleagues: David van Zeyl, Matthieu Sturzenegger and Andrew Beveridge. It

was a great pleasure working with them and I appreciate their ideas, help and good

humour. Special thanks goes to Roderick Tollenaar for sharing valuable data.

My deepest appreciation belongs to my family for their patience and understanding.

With regards to numerous questions about my future academic endeavours from

family and friends I shall answer in the words of Sir Winston Churchill: “Now, this is

not the end. It is not even the beginning of the end. But it is, perhaps, the end of

the beginning”.


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TABLE OF CONTENTS

Approval ................................................................... Error! Bookmark not defined.

Abstract ............................................................................................................... ii

Dedication .......................................................................................................... iv

Acknowledgements ............................................................................................ v

Table of Contents .............................................................................................. vi

List of Figures ..................................................................................................... x

List of Tables ................................................................................................. xviii

Chapter 1: Introduction ...................................................................................... 1

1.1 Block Caving Mining and Associated Surface Subsidence ................ 1

1.2 Research Objectives .......................................................................... 3

1.3 Thesis Organization ........................................................................... 4

Chapter 2: Literature Review ............................................................................. 6

2.1 Introduction ........................................................................................ 6

2.2 Stages of Subsidence Development and Associated Rock Mass Failure Mechanisms .................................................................. 7

2.3 Subsidence Characterization ............................................................. 9

2.4 Factors Governing Subsidence Development .................................. 12

2.5 A Block Caving Subsidence Analysis Toolbox ................................. 15

2.5.1 Empirical Methods ........................................................................ 15

2.5.2 Limit Equilibrium Techniques ........................................................ 17

2.5.3 Numerical Approaches .................................................................. 21

2.6 Summary .......................................................................................... 29

Chapter 3: Research Methodology and Theory ............................................. 31

3.1 Introduction ...................................................................................... 31

3.2 Modelling Approach Selection .......................................................... 31

3.2.1 Analysis of Available Modelling Approaches ................................. 31

3.2.2 Fracture Mechanics Based Hybrid Continuum/Discontinuum Approach ....................................................................................... 33

3.3 Fundamentals of Fracture Mechanics .............................................. 34

3.4 Implementation of the Hybrid Continuum-Discontinuum with Fracture Approach in the ELFEN Code .............................................. 36

3.4.1 Solution Procedure for Continuum to Discontinuum Transition ...................................................................................... 37

3.4.2 Constitutive Models for Rock Material ........................................... 38


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3.4.3 Continuum Degradation through Fracturing .................................. 41

3.4.4 Contacts Interaction Handling ....................................................... 43

3.4.5 Applications of ELFEN in Rock Engineering ................................. 44

3.5 Rock Mass Representation Options in Context of Fracture Mechanics Based FEM/DEM Modelling ........................................... 45

3.6 Integrated Use of Discrete Fracture Network Models and ELFEN Code .................................................................................... 47

3.6.1 DFN Approach to Discontinuity Representation ............................ 47

3.6.2 Integration of DFN Models into ELFEN ......................................... 49

3.7 General Considerations in Modelling Methodology .......................... 51

3.8 Summary .......................................................................................... 51

Chapter 4: Use of Equivalent Continuum Rock Mass Properties in the Discrete Fracture Network FEM/DEM Modelling of Block Caving Induced Subsidence ......................................................................................... 52

4.1 Introduction ...................................................................................... 52

4.2 Rock Mass Equivalent Continuum Mechanical Properties ............... 52

4.3 Derivation of Rock Mass Mechanical Properties ................................. 54

4.3.1 Analytical Methods ........................................................................ 54

4.3.2 In-situ Testing ............................................................................... 55

4.3.3 Numerical Modelling ..................................................................... 55

4.3.4 Empirically Based Rock Mass Classification Systems. ................. 56

4.4 Comparative Study of Rock Mass Strength and Deformability Parameters Derived through RMR76, GSI and Q Rock Mass Classification Systems ...................................................................... 60

4.4.1 Properties Derivation .................................................................... 60

4.4.2 Rock Mass Deformation Modulus ................................................. 64

4.4.3 Rock Mass Friction Angle ............................................................. 65

4.4.4 Rock Mass Cohesion .................................................................... 66

4.4.5 Rock Mass Tensile Strength ......................................................... 66

4.4.6 Summary ...................................................................................... 67

4.5 Evaluation of Applicability of Rock Mass Classifications Derived Equivalent Continuum Properties for Modelling of Block Caving Induced Surface Subsidence .............................................................. 68

4.5.1 Modelling Methodology ................................................................. 68

4.5.2 Constraining Criteria ..................................................................... 74

4.5.3 Modelling Results .......................................................................... 76

4.5.4 Conclusions .................................................................................. 89

4.6 Summary .......................................................................................... 89

Chapter 5: Conceptual Modelling Study of the Factors Controlling Block Caving Subsidence Development ......................................................... 91

5.1 Introduction ...................................................................................... 91

5.2 Model Setup and Analysis Strategy .................................................. 91

5.3 Influence of Jointing ......................................................................... 93

5.3.1 Effect of Joint Orientation .............................................................. 93

5.3.2 Effect of Joint Persistence .......................................................... 108


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5.3.3 Effect of Joint Shear and Normal Stiffness ................................. 111

5.4 Influence of Faults .......................................................................... 114

5.4.1 Effect of Fault Location ............................................................... 114

5.4.2 Effect of Fault Inclination ............................................................. 127

5.5 Influence of Rock Mass Strength and Deformability Characteristics ................................................................................ 137

5.6 Influence of Stress Environment ..................................................... 142

5.7 Influence of Varying Lithological Domains ...................................... 147

5.7.1 Effect of Varying Strength between Ore and Host Rock ............. 147

5.7.2 Effect of Varying Joint Orientation within the Ore and Host Rock ............................................................................................ 154

5.8 Influence of Block Depth and Excavation Volume .......................... 160

5.9 Results Synthesis ........................................................................... 169

5.10 Summary ........................................................................................ 178

Chapter 6: Block Caving Induced Instability in Large Open Pit Slopes .... 179

6.1 Introduction .................................................................................... 179

6.2 Transition from Open Pit to Block Cave Mining .............................. 179

6.3 Characteristic Slope Failure Mechanisms in Large Open Pits ........ 181

6.4 Conceptual Study of Block Caving Induced Step-path Driven Failure in Large Open Pit Slope ..................................................... 187

6.4.1 Modelling Methodology ............................................................... 187

6.4.2 Modelling Results ........................................................................ 190

6.4.3 Conclusions ................................................................................ 200

6.5 Preliminary Modelling of Block Caving Induced Failure of the North Wall, Palabora mine ............................................................. 201

6.5.1 Problem Description .................................................................... 201

6.5.2 General Approach in the Current Modelling Analysis.................. 207

6.5.3 Model Setup ................................................................................ 208

6.5.4 Modelling Results and Discussion .............................................. 211

6.5.5 Conclusions ................................................................................ 215

6.6 Summary ........................................................................................ 215

Chapter 7: Conclusions and Recommendations for Further Research ..... 217

7.1 Conclusions .................................................................................... 217

7.1.1 Current State of Knowledge of Block Caving Induced Subsidence ................................................................................. 217

7.1.2 FEM/DEM-DFN Approach to Subsidence Analysis..................... 218

7.1.3 Modelling Input Parameters ........................................................ 219

7.1.4 Factors Governing Block Caving Subsidence Development ....... 220

7.1.5 Large Open Pit - Block Caving Interaction .................................. 221

7.2 Key Scientific Contributions ............................................................ 222

7.3 Recommendations for Further Research ....................................... 223

7.3.1 Equivalent Continuum Rock Mass Properties ............................. 223

7.3.2 Modelling of 3D Aspects of Block Caving Subsidence Development ............................................................................... 223

7.3.3 ELFEN Code Enhancements ...................................................... 223


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7.3.4 In-situ Subsidence Characterization ........................................... 224

Reference List ................................................................................................. 225

Appendix A. Preliminary Statistical Summary of Conceptual Study Modelling Results ............................................................................................ 237

Appendix B. DFN Parameters for Palabora Model ....................................... 239

Appendix C. Development of North Wall Failure at Palabora mine (photos) ........................................................................................................... 240


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LIST OF FIGURES

Fig. 1.1 Typical block caving mine layout. .......................................................... 2

Fig. 1.2 Caving initiation and ore extraction. ....................................................... 2

Fig. 1.3 Block caving mining and associated surface subsidence. ..................... 2

Fig. 2.1 Development of surface subsidence induced by block caving ............... 8

Fig. 2.2 Block caving subsidence characterization terminology ........................ 10

Fig. 2.3 Example of surface subsidence zonation at Northparkes mine ........... 10

Fig. 2.4 Relative frequency of break angles for different rock mass qualities (Laubscher‟s RMR), in the subsidence craters of underground mines by caving methods ............................................... 12

Fig. 2.5 Beneficial and detrimental effects of major weakness planes ............. 15

Fig. 2.6 Empirical chart relating MRMR and cave (break) angle ...................... 16

Fig. 2.7 Progressive hanging wall failure sequence with increasing depth of mining .............................................................................................. 17

Fig. 2.8 Idealised model for limit equilibrium analysis of progressive hangingwall caving .............................................................................. 18

Fig. 2.9 Toppling of steeply dipping hangingwall strata .................................... 20

Fig. 2.10 Example of problem discretization using FEM ..................................... 22

Fig. 2.11 Various approaches to model rock engineering problems: (a) continuum, (b) discrete and (c) hybrid ................................................. 23

Fig. 2.12 Design chart for estimation the angle of break in a transition from open pit to underground mining by block/panel caving ........................ 27

Fig. 3.1 Fracture mechanics basic crack tip loading modes (based on Whittaker et al., 1992). ........................................................................ 34

Fig. 3.2 Rankine Rotating Crack model: (a) yield surface and (b) softening curve .................................................................................... 39

Fig. 3.3 Yield surface for the conventional Mohr Coulomb model .................... 39

Fig. 3.4 Yield surfaces for (a) Mohr Coulomb and (b) Mohr Coulomb with Rankine tensile cut-off criteria ............................................................. 40

Fig. 3.5 Crack insertion in ELFEN .................................................................... 43


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Fig. 3.6 Comparison of contacts interaction handling in DEM and FEM/DEM methods ............................................................................. 44

Fig. 3.7 DFN model development workflow ...................................................... 49

Fig. 3.8 Example of a FracMan model (adapted after Elmo, 2006, with permission) .......................................................................................... 50

Fig. 4.1 RMR, Q and rock mass deformation modulus correlations ................. 58

Fig. 4.2 GSI and rock mass deformation modulus correlation proposed by Hoek & Diederichs (2006) ............................................................... 58

Fig. 4.3 Comparison of rock mass strength and deformability characteristics derived using RMR76, Q and GSI RMC systems ......... 63

Fig. 4.4 Percentile change in properties magnitudes with increasing rock mass rating .......................................................................................... 64

Fig. 4.5 ELFEN model setup and response evaluation procedure ................... 70

Fig. 4.6 Physical model of progressive caving development (adapted after Kvapil, 2004 with permission). ..................................................... 71

Fig. 4.7 Derivation of joints shear stiffness using Barton‟s (1982) correlation ............................................................................................ 73

Fig. 4.8 Constraints for ELFEN modelling of block caving induced subsidence .......................................................................................... 76

Fig. 4.9 Caving response with RMR equivalent continuum properties ............. 80

Fig. 4.10 Caving response with Q equivalent continuum properties (90% tensile c.o.) .......................................................................................... 81

Fig. 4.11 Caving response with Q equivalent continuum properties (70% tensile c.o.) .......................................................................................... 82

Fig. 4.12 Caveability assessment using Laubscher‟s chart for studied equivalent continuum properties .......................................................... 83

Fig. 4.13 Simulation of cave development progression for RMR equivalent continuum properties. .......................................................................... 84

Fig. 4.14 Simulation of cave development progression for Q (90% tensile cut-off) equivalent continuum properties. ............................................. 85

Fig. 4.15 Simulation of cave development progression for Q (70% tensile cut-off) equivalent continuum properties. ............................................. 86

Fig. 4.16 Simulation of subsidence development with RMR equivalent continuum properties. .......................................................................... 87

Fig. 4.17 Simulation of subsidence development with Q equivalent continuum properties. .......................................................................... 88

Fig. 5.1 Assumed fracture orientations for BC (a), J1 (b), J2 (c), J3 (d) and J4 (e) models ................................................................................ 94


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Fig. 5.2 Subsidence crater formation for Base Case (a) and J1(b) models ...... 96

Fig. 5.3 Subsidence crater formation for J2 (a) and J3 (b) models ................... 97

Fig. 5.4 Subsidence crater formation for J4 model ........................................... 98

Fig. 5.5 Variation of vertical stress (Pa) contours with caving at 5% ore extraction for Base Case and J2 models ............................................. 98

Fig. 5.6 Subsidence at 100% ore extraction for BC (a), J1 (b), J2 (c), J3 (d) & J4 (e) models ............................................................................ 101

Fig. 5.7 Surface profiles at the end of ore extraction for BC, J1, J2, J3 and J4 models ................................................................................... 102

Fig. 5.8 Subsidence characterization for Base Case, J1, J2, J3 and J4 models ............................................................................................... 104

Fig. 5.9 Evolution of zone of major (≥10cm) vertical (YY) and horizontal (XX) surface deformations with continuous ore extraction for Base Case (a), J1 (b), J2 (c), J3 (d) and J4 (e) models ..................... 105

Fig. 5.10 Rate of growth of 10cm surface displacement zone west of the block centre vertical axis with continuous ore extraction for Base Case, J1, J2, J3 and J4 models ......................................................... 106

Fig. 5.11 Total vertical (a) and horizontal (b) surface displacements at the end of ore extraction at different distances from block centre for Base Case, J1, J2, J3 and J4 models ............................................... 106

Fig. 5.12 Subsidence at 100% ore extraction for J5 (a) and J6 (b) models ...... 109

Fig. 5.13 Subsidence characterization for J2, J5 and J6 models ...................... 110

Fig. 5.14 Total vertical (a) and horizontal (b) surface displacements at the end of ore extraction at different distances from block centre for J2, J5 and J6 models ......................................................................... 110

Fig. 5.15 Subsidence at 100% ore extraction for J7 and J8 model ................... 112

Fig. 5.16 Subsidence characterization for Base Case, J7, J2 and J8 models ............................................................................................... 112

Fig. 5.17 Total vertical (a) and horizontal (b) surface displacements at the end of ore extraction at different distances from block centre for Base Case, J1, J2, J3 and J4 models ............................................... 113

Fig. 5.18 Assumed fracture orientations and fault positions for F1 to F9 models ............................................................................................... 115

Fig. 5.19 Subsidence crater formation for F1 model ......................................... 116





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Fig. 5.24 Subsidence at 100% ore extraction for F1, F2, F3, F4 and F5 model ................................................................................................. 121

Fig. 5.25 Subsidence characterization for Base case, F1, F2 and F3 .............. 124

Fig. 5.26 Subsidence characterization for J2, F4 and F5 ................................. 124

Fig. 5.27 Total vertical (a) and horizontal (b) surface displacements at the end of ore extraction at different distances from block centre for Base Case, F1, F2 and F3 models .................................................... 125

Fig. 5.28 Total vertical (a) and horizontal (b) surface displacements at the end of ore extraction at different distances from block centre for J2, F4 and F5 models ........................................................................ 125

Fig. 5.29 Differential XY displacements for surface points on the fault hanging and footwalls: (a) F1, F2 and F3; (b) F4 and F5 models ...... 126





Fig. 5.34 Subsidence at 100% ore extraction for F6, F7, F8 and F9 models .... 132

Fig. 5.35 Subsidence characterization for BC, F2, F6 and F7 models ............. 134

Fig. 5.36 Subsidence characterization for J2, F4, F8 and F9 models ............... 135

Fig. 5.37 Total vertical (a) and horizontal (b) surface displacements at the end of ore extraction at different distances from block centre for Base Case, F2, F6 and F7 models .................................................... 135

Fig. 5.38 Total vertical (a) and horizontal (b) surface displacements at the end of ore extraction at different distances from block centre for J2, F4, F8 and F9 models .................................................................. 136

Fig. 5.39 Differential XY displacements for surface points on the fault hanging and foot walls for F2, F6 and F7 models .............................. 136

Fig. 5.40 Stages of subsidence crater formation at different percentages of ore block extraction for model RM2 ................................................... 139

Fig. 5.41 Subsidence at 100% ore extraction for models RM1, RM2 and RM3 ................................................................................................... 140

Fig. 5.42 Subsidence characterization for models J2, RM1, RM2 and RM3..... 141

Fig. 5.43 Total vertical (a) and horizontal (b) surface displacements at the end of ore extraction at different distances from block centre for models J2, RM1, RM2 and RM3 ........................................................ 141


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Fig. 5.44 Subsidence at 100% ore extraction for models S1, S2, S3 and S4 ...................................................................................................... 144

Fig. 5.45 Subsidence characterization for models Base Case, S1 and S2 ....... 145

Fig. 5.46 Subsidence characterization for models J2, S3 and S4 .................... 145

Fig. 5.47 Total horizontal surface displacements at the end of ore extraction at different distances from block centre for models Base Case, S1 and S2 ...................................................................... 146

Fig. 5.48 Total vertical (a) and horizontal (b) surface displacements at the end of ore extraction at different distances from the block centre for models J2, S3 and S4 .................................................................. 146

Fig. 5.49 Assumed geometries for models GD1 to GD4................................... 147

Fig. 5.50 Subsidence crater formation for models (a) GD1 with a caprock and (b) GD2 without a caprock .......................................................... 149

Fig. 5.51 Subsidence crater formation for models (a) GD3 with a caprock and (b) GD4 without a caprock .......................................................... 150

Fig. 5.52 Subsidence at 100% ore extraction for models (a) GD1, (b) GD2, (c) GD3 and (d) GD4 ......................................................................... 151

Fig. 5.53 Subsidence characterization for models Base Case, GD1 and GD2 ................................................................................................... 153

Fig. 5.54 Subsidence characterization for models J2, GD3 and GD4 .............. 153

Fig. 5.55 Total vertical (a) and horizontal (b) surface displacements at the end of ore extraction at different distances from block centre for models J2, GD3 and GD4 ................................................................. 154

Fig. 5.56 Assumed modelling geometries for models (a) GD5 and (b) GD6..... 155

Fig. 5.57 Subsidence crater formation for models GD5 and GD6 .................... 157

Fig. 5.58 Subsidence at 100% ore extraction for models GD5 and GD6 .......... 158

Fig. 5.59 Subsidence characterization for models Base Case, J2, GD5 and GD6 ............................................................................................ 158

Fig. 5.60 Total vertical (a) and horizontal (b) surface displacements at the end of ore extraction at different distances from block centre for models Base Case, J2, GD5 and GD6 .............................................. 159

Fig. 5.61 Subsidence crater formation for models BD1 and BD2 ..................... 161

Fig. 5.62 Subsidence at 100% and 150% for BD1 model ................................. 162

Fig. 5.63 Subsidence at 150% ore extraction for Base Case model ................. 163

Fig. 5.64 Subsidence at 100% (a) and 150% (b) for BD2 model ...................... 163

Fig. 5.65 Subsidence at 150% ore extraction for J2 model .............................. 164


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Fig. 5.66 Comparison of surface profiles and angles limiting major surface deformations for models with varying block depth and joint inclination at 100% ore extraction ...................................................... 165

Fig. 5.67 Surface profiles at the end of ore extraction for BC (100%), BC (150%), BD1 (100%) and BD1 (150%) models.................................. 165

Fig. 5.68 Surface profiles at the end of ore extraction for J2 (100%), J2 (150%), BD2 (100%) and BD2 (150%) models.................................. 165

Fig. 5.69 Subsidence characterization for models BC (100%), BC (150%), BD1 (100%) and BD1 (150%)............................................................ 167

Fig. 5.70 Subsidence characterization models J2 (100%), J2 (150%), BD2 (100%) and BD2 (150%) ................................................................... 167

Fig. 5.71 Total vertical (a) and horizontal (b) surface displacements at the end of ore extraction at different distances from block centre for BC (100%), BC (150%), BD1 (100%) and BD1 (150%) models ........ 168

Fig. 5.72 Total vertical (a) and horizontal (b) surface displacements at the end of ore extraction at different distances from block centre for J2 (100%), J2 (150%), BD2 (100%) and BD2 (150%) models .......... 168

Fig. 5.73 Comparative summary of modelling results - total extent of major (≥10cm) surface displacements ......................................................... 171

Fig. 5.75 Comparative summary of modelling results - minimum angles delineating the extent of major (≥10cm) surface displacements, asymmetry index ............................................................................... 173

Fig. 5.76 Comparative summary of modelling results – volume of the rock mass mobilized by the caving ............................................................ 174

Fig. 6.1 Slope failure modes (based on Sjöberg, 1999).................................. 183

Fig. 6.2 Comparison of limit equilibrium analysis of planar and step-path failure (modified after Eberhardt et al., 2004a, with permission) ........ 184

Fig. 6.3 The pit-slope proximity problem: preliminary brittle fracture analysis (adapted after Stead et al., 2007, with permission) ............. 186

Fig. 6.4 Typical model geometry for simulation of block caving induced step-path failure (cases with two rock bridges shown). ..................... 188

Fig. 6.5 Block caving induced step-path failure in large open pit slope (model M1) ........................................................................................ 191

Fig. 6.6 Maximum principal stress contours (Pa) - tensile stress concentrations (red) in rock bridges prior to failure ............................ 192

Fig. 6.7 Typical rock bridge failure development ............................................ 192

Fig. 6.8 Stress/displacement analysis of caving - open pit slope interaction (rock bridges failure, model M1) ....................................... 193


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Fig. 6.9 Stress/displacement analysis of caving - open pit slope interaction (rock bridge failure, model M2) ........................................ 194

Fig. 6.10 Stress/displacement analysis of caving - open pit slope interaction (rock bridge failure, model M3) ........................................ 194

Fig. 6.11 Block caving induced rock step-path failure in large open pit slope (model M4) ............................................................................... 196

Fig. 6.12 Block caving induced step-path failure in large open pit slope (model M5) ........................................................................................ 197



Fig. 6.15 Development of step-path failure in the open pit slope during caving mining with relation to crown pillar geometry and stress level for simulations with different % of rock bridges in step-path failure surface .................................................................................... 199

Fig. 6.16 Variation of vertical stress in the crown pillar (50m below pit bottom) for models M1-M5................................................................. 200

Fig. 6.17 3D view of Palabora pit and cave mine (adapted after Brummer et al., 2005, with permission) ............................................................. 202

Fig. 6.18 General geology and pit slope geometry at Palabora mine (adapted after Moss et al., 2005, with permission) ............................ 204

Fig. 6.19 Major geological structures at Palabora mine (based on data provided by Palabora Mining Company Limited) ............................... 204

Fig. 6.20 Plan view of North Wall failure at Palabora mine ............................... 206

Fig. 6.21 Preliminary DFN model of Palabora mine North Wall section ........... 209

Fig. 6.22 ELFEN model of Palabora mine NW-SE section (section A-A in Fig. 6.20). .......................................................................................... 210

Fig. 6.23 Pit slope deformation at cave breakthrough for model P1 ................. 213

Fig. 6.24 Pit slope deformation at 40% ore extraction for model P1 ................. 213

Fig. 6.25 Pit slope deformation at cave breakthrough for model P2 ................. 214

Fig. 6.26 Pit slope deformation at 40% ore extraction for model P2 ................. 214

Fig. A.1 Probability (relative frequency) of the caving induced total extent of major (≥10cm) vertical surface displacements based on 37 model runs. ........................................................................................ 237

Fig. A.2 Probability of the caving induced total extent of major (≥10cm) horizontal surface displacements. ..................................................... 237


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Fig. A.3 Probability of rock mass volume mobilized by caving, in percent of extracted ore volume. .................................................................... 238

Fig. A.4 Probability of minimum angles delineating the extent of caving induced major surface displacements. .............................................. 238

Fig. A.5 Probability of subsidence asymmetry index. ...................................... 238

Fig. C.1 Bench failure at the bottom of the pit - July 2004............................... 240

Fig. C.2 Developing failure of the North Wall - October 7th, 2004. .................. 241

Fig. C.3 Failed North Wall – late May, 2005. ................................................... 241


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LIST OF TABLES

Table 2.1 Degree of influence of various factors affecting surface subsidence development suggested by Flores & Karzulovic (2002). ................................................................................................. 13

Table 2.2 Evolution of limit equilibrium methods of subsidence analysis ........... 19

Table 2.3 Numerical methods and proprietary codes widely applied in rock engineering .................................................................................. 24

Table 2.4 Numerical studies of caving induced surface subsidence. ................. 25

Table 3.1 Hybrid continuum-discontinuum with fracture modelling approach ............................................................................................. 33

Table 3.2 Fracture toughness and fracture energy values for various rock types .................................................................................................... 36

Table 4.1 Rock mass parameters used in rock mass rating by RMR76, Q and GSI ............................................................................................... 56

Table 4.2 Empirical relationships for derivation of estimates of basic rock mass strength and deformability properties based on the RMR, GSI and Q rock mass classification systems ................................................ 57

Table 4.3 Rock mass properties derived using RMR76 ....................................... 61

Table 4.4 Rock mass properties derived using Q ............................................... 62

Table 4.5 Rock mass properties derived using GSI ............................................ 62

Table 4.6 List of principal modelling scenarios and corresponding input parameters ........................................................................................... 74

Table 5.1 Modelling input parameters ................................................................ 92

Table 5.2 Modelling scenarios for analysis of the effect of joint orientation ......... 93

Table 5.3 Modelling scenarios for analysis of the effect of fault location ........... 114

Table 5.4 Modelling scenarios for analysis of the effect of fault inclination ........ 127

Table 5.5 Modelling scenarios for analysis of the effect of stress environment ....................................................................................... 142

Table 5.6 Modelling scenarios for analysis of the effect of varying strength between ore and host rock ................................................................. 148

Table 5.7 Modelling scenarios for analysis of the effect of varying joint orientation within the ore and host rock .............................................. 155


xix

Table 5.8. Preliminary classification of caving induced surface subsidence for cases with no major geological discontinuities ................................ 175

Table 5.9. Preliminary classification of the influence of major geological discontinuities on caving induced surface subsidence.......................... 176

Table 5.10. Initial influence assessment matrix of factors contributing to block caving induced surface subsidence ............................................ 177

Table 6.1 Modelling input parameters used in conceptual modelling ................ 189

Table 6.2 Modelling scenarios ......................................................................... 189

Table 6.3 Description of rock units present in the North Wall ............................ 203

Table 6.4 Modelling input parameters for preliminary Palabora failure simulation ........................................................................................... 211

Table B.1 Description of rock units present in the North Wall ........................... 239


1

CHAPTER 1: INTRODUCTION

1.1 Block Caving Mining and Associated Surface Subsidence

Block caving is one of the most cost effective underground mining techniques; it

largely relies on managing the forces of nature to extract the ore. Block caving is

typically employed to mine massive low grade copper, gold and molybdenum

mineralization and diamond-bearing kimberlite pipes. High efficiency and low

production costs coupled with ever growing demand on natural resources are

making the block caving method increasingly important for the mining industry. It

is anticipated that in the next ten years the number of major block caving

operations will double. This will involve development of new block caving mines,

as well as the transition of existing large open pit mines reaching economic limits

to underground mining, utilizing the block caving method.

A typical block caving mine layout, shown in Fig. 1.1, consists of two mining levels

(production level and undercut level) placed within the ore column. In block caving,

ore is mined sequentially in large sections (blocks), with areas of several thousands

of square metres. Caving is initiated by blasting an extensive horizontal panel

(undercut) under the mined block. Stress redistribution and gravity combine to trigger

progressive fracturing and caving of the ore into the undercut. As caving of the ore is

initiated, the undercut is connected with the production level by blasting bell-shaped

ore passages, called drawbells, each consisting of at least two drawpoints (see Fig.

1.2). Broken ore falls through the drawpoints into the production level where it is

picked up and transported to the crusher and subsequently brought to the surface.

As broken ore is removed from the drawpoints, the ore above continues to break and

cave in by gravity, as illustrated in Fig. 1.3. Caving progressively extends upwards

as the ore is extracted, causing significant surface depression, or subsidence, above

the undercut and in the adjacent areas. In open pit/caving environments this may

trigger instability in open pit slopes.


2

Fig. 1.1 Typical block caving mine layout.

Fig. 1.2 Caving initiation and ore extraction.

Fig. 1.3 Block caving mining and associated surface subsidence.

Note: Figs. 1.1 - 1.3 are block caving animation screenshots modified after Sandvik Corp. with permission.

caving ore

surface subsidence

3

According to Brady & Brown (2004) some instances of block caving mining

induced subsidence have had dramatic consequences, including loss of life, loss

of parts of producing mines and loss of major surface installations. In addition,

as indicated by Blodgett & Kuipers (2002), changes to surface landforms brought

about by block caving subsidence can be quite dramatic and may lead to a

pronounced environmental impact.

1.2 Research Objectives

The ability to predict surface subsidence associated with block caving mining is

important for mine planning, operational hazard assessment and evaluation of

environmental and socio-economic impacts. Owing to problems of scale and

lack of access, our fundamental understanding of the complex rock mass

response leading to subsidence development is limited at best as are our current

subsidence prediction capabilities.

In light of increasing use of the block caving mining method and the importance of

knowledge of potential surface subsidence there is a genuine need for an inclusive

study on surface subsidence associated with block caving. Current knowledge of

subsidence phenomena can be improved by employing numerical modelling

techniques. These provide a convenient framework for enhancing our understanding

of the basic factors governing the mechanisms of subsidence, an essential

prerequisite if advances in the prediction of subsidence are to be made.

This thesis has three principal research objectives:

1. Introduce a new methodology for the numerical analysis of surface

subsidence associated with block caving mining;

2. Improve understanding of subsidence phenomena and rock mass

behaviour in block caving settings through thorough analysis of factors

that may govern subsidence development;

3. Investigate mechanisms of block caving induced instability in large open pit

mine slopes.

4

1.3 Thesis Organization

The dissertation consists of seven chapters. This introductory chapter, which

poses the research problem and thesis objectives is followed by a

comprehensive literature review, presented in Chapter 2. This review

summarizes the current state of knowledge of subsidence phenomena, critically

evaluates the available methods of subsidence analysis and outlines previous

work undertaken in this area.

Chapter 3 discusses the available modelling approaches for simulation of block

caving surface subsidence phenomena and introduces the finite/discrete element

method (FEM/DEM) with fracture propagation code used in the current analysis.

An overview of the fundamentals of fracture mechanics is provided as well as an

outline of the implementation of this approach in the proprietary code ELFEN.

The advantages of this type of geomechanical modelling are highlighted and its

integration with Discrete Fracture Networks (DFN) is discussed and the proposed

modelling methodology is outlined.

Chapter 4 addresses the question of selection of equivalent rock mass properties

for the adopted FEM/DEM-DFN modelling technique. It discusses available

approaches to the derivation of jointed rock mass mechanical properties and

examines the properties output from rock mass classification systems. An analysis

of rock mass representation options within FEM/DEM modelling is given and a

novel approach to the derivation and calibration of rock mass properties

specifically tailored for block caving subsidence analysis using integrated DFN-

FEM/DEM modelling is presented.

Chapter 5 gains fundamental understanding of the block caving subsidence

phenomenon through a thorough conceptual FEM/DEM-DFN modelling analysis

of the factors controlling surface subsidence development, including: geological

structure (jointing and faults), rock mass strength, in-situ stress level, mining depth,

volume of extracted material and varying lithological domains. The discussion and

conclusions on the role of individual factors are provided. Synthesis of the

modelling results is presented in terms of preliminary classification of the caving

5

induced surface subsidence, classification of the role of major geological

discontinuities and an influence assessment matrix providing qualitative

assessment of the relative importance of individual factors affecting block

subsidence.

Chapter 6 addresses the problem of slope instability/subsidence in a large

overlying open pit associated with block caving mining, focusing on the analysis of

caving induced step-path failure in the pit slope. It uses a comprehensive “total

interaction” analysis approach, allowing to relate cave propagation, development of

the failure within the slope and the resultant surface subsidence. The FEM/DEM-

DFN modelling methodology is applied to the analysis of the complex mechanism

of caving induced open pit slope failure at Palabora mine.

Finally, Chapter 7, contains research conclusions, outlines key scientific

contributions of this work and discusses further research avenues.

6

CHAPTER 2: LITERATURE REVIEW

2.1 Introduction

Brady & Brown (2004) defined subsidence as the lowering of the ground surface

following the underground extraction of ore or another reserve. They suggested

that there are two types of subsidence deformation: continuous and discontinuous.

Continuous subsidence is usually associated with longwall mining, employed for

the extraction of thin, horizontal or flat-dipping orebodies overlain by weak

sedimentary strata, and is characterized by a formation of relatively smooth

surface depression. Block caving mining is typically utilized in hard rock

environments and involves extraction of massive volumes of ore and is

characterized by discontinuous subsidence. In this case, large scale surface

displacements manifest in formation of a crater and stepped terraces or major

discontinuities on the surface profile.

Underground mining induced surface subsidence has been discussed extensively

in the literature, however this has primarily focused on the analysis of continuum

subsidence associated with longwall coal mining. There is a wealth of literature on

this topic including textbooks (Kratzsch, 1983; Whittaker & Reddish, 1989; Peng,

1992) and a subsidence engineering handbook (National Coal Board, 1975). In

marked contrast the literature on block caving induced discontinuum surface

subsidence is more limited and our state of understanding of the phenomena

certainly does not allow confident prediction in the form of handbooks.

The objective of this chapter is to summarize the current state of knowledge on

caving induced discontinuum surface subsidence. The following themes are

discussed:

stages in surface subsidence development and associated rock mass

failure mechanisms;

7

subsidence characterization;

factors influencing surface subsidence development; and

existing methods of caving induced subsidence analysis. (Block Caving

subsidence toolbox).

2.2 Stages of Subsidence Development and Associated Rock Mass Failure Mechanisms

Block caving derived surface movements are caused by the progressive failure of

the caved rock into the void left by extracted ore. A conceptual model of block

caving induced subsidence development is shown in Fig. 2.1 based on key stages

of subsidence after cave initiation as proposed by Abel & Lee (1980).

1. Collapse of rock progresses upward from the extraction level as ore is

withdrawn from below. The resulting column of caved and broken rock is

restricted above the area of extraction.

2. The ground surface does not measurably begin to subside until caving has

so thinned the overlying cap rock that it cannot transfer the load from this

rock onto the adjacent solid cave walls. The overlying rock will thus begin

to deflect downward toward the caved rock below. Lateral movement of

adjacent rock into the ore column is resisted by the active (and possibly

passive) pressure of the caved muck pile.

3. Further extraction of caved ore from below results in increased

subsidence of the ground surface above and adjacent to the area of

extraction. The overlying intact rock is progressively thinned by further

propagation of the cave back.

4. Continued extraction of ore will result in breaching of the surface. The

initial breach is typically in the form of a circular pit, commonly referred to

as a chimney cave breakthrough. The breakthrough is roughly centered

over the mining area although offsets may occur if geologic weaknesses

are present.

8

5. If ore extraction continues, the surface breach will grow laterally near the

surface. The rock adjacent to the subsided chimney either slides along

geologic weaknesses, such as joints or faults, or topples into the open crater.

Fig. 2.1 Development of surface subsidence induced by block caving

(modified after van As, 2003, with permission)

Woodruff (1966), Hoek (1974), Brown & Ferguson (1979) and Singh et al. (1993)

stated that during caving the main rock failure mechanisms are shear, tension or

a combination of the two. Based on numerical modelling studies Singh et al.

(1993) suggested that in the absence of major geologic structures, the dominant

mode of rock failure in progressive caving is tension. The gravity load results in

tensile stresses in the rock mass close to the surface, when the strain limit of the

rock mass is exceeded, tensile fractures develop. If major geological structures

are present, and appropriately oriented, the dominant failure mode is likely to be

shear failure along these surfaces.

a. Caving initiation b. Cave advance towards surface

c. Formation of surface depression d. Cave breakthrough and crater development

9

2.3 Subsidence Characterization

Following surveys of the recent literature on block caving subsidence van As

(2003) and Flores & Karzulovic (2004) noted a scatter of opinions and to some

degree even confusion in the use of caving subsidence terminology (principally

due to a lack of standardization across the mining industry). These authors

unfortunately proposed two somewhat different subsidence characterization

terminology standards and a consensus has yet to be attained. In the current

study, a more descriptive block caving subsidence terminology proposed by van

As (2003), shown in Fig. 2.2, is adopted. An example of using this terminology for

characterization of subsidence at Northparkes Mines (Australia) is illustrated in Fig.

2.3.

The terminology proposed by van As (2003) is largely based on the work of Lupo

(1998), who conceptualized surface deformations observed and/or measured at

several caving mines into three distinctive zones:

Caved rock zone

Large-scale cracking zone (fractured zone in van As (2003) terminology)

Continuous subsidence zone

The caved rock zone corresponds to a zone of active cave movement. It is

typically situated above the active caving footprint and usually is manifested as a

crater. The material in this zone comprises caved ore and waste rock which has

broken up into irregular blocks and fines. As indicated by Laubscher (1981) this

caved material provides lateral restraint to the crater wall reducing the extent of

subsidence deformations. With continuing ore extraction this restraint is

gradually removed and the extent of surface deformations will grow. Total

surface subsidence in the caved rock zone over the life span of the mine may

reach several tens of metres.

The large scale cracking or fractured zone is characterized by an irregular broken

surface with scarps (produced as a result of rotational overturning), large open

tension cracks, benches and large blocks undergoing shear-rotational and toppling

failure into the crater.

10

Fig. 2.2 Block caving subsidence characterization terminology

(modified after van As, 2003, with permission)

Stable ZoneStable Zone

Stable Zone

Unstable Zone

Unstable Zone

Breakthrough Zone

Continuous Subsidence Zonetension cracks

caved rock or crater zone

fractured zone

continuous subsidence zone

Fig. 2.3 Example of surface subsidence zonation at Northparkes mine

(modified after van As, 2003 with permission)

11

The continuous subsidence zone is characterised by a gentle surface depression

which may also involve minor cracking. The surface deformations within this

zone are relatively small in comparison to other zones, although, they should not

be neglected in mine planning. Lupo (1998) reported subsidence of up to

200mm in a continuous subsidence zone which caused significant damage in

nearby structures.

As illustrated in Fig. 2.2 the boundaries between different deformation zones are

defined by three limiting angle drawn from the edge of the undercut: angles of

break, angle of fracture initiation and angle of subsidence.

The angle of break measures the extent of the caved rock zone or the boundary

of the caved material. According to van As (2003) mining experience suggests

the following common trends regarding this angle:

it increases with depth; and

it tends to be sub-vertical in strong rocks with no significant inclined

discontinuities, and inclined where mining depths are shallow and/or

overburden rocks are weak.

Flores & Karzulovic (2002) based on the subsidence data from ten caving

operations, related rock mass quality and break angle as shown in Fig. 2.4. As

apparent from this figure:

the angle of break tends to increase with rock mass quality;

most angle of break data are in a range of 50° to 90°; and

for a rock mass with a Modified Rock Mass Rating (MRMR) > 70 the angle

of break tends to be larger than 60°.

The fracture initiation angle measures the extent of major surface cracking,

where the ground is already failed or potentially unstable. In his summary of

block caving subsidence observations, based on limited sources, van As (2003)

reported fracture initiation angles in the range of 25° to 80°.

The angle of subsidence defines the limits of surface deformations. It should be

noted that this information is rarely collected. Based on the data from studied caving

12

mines Lupo (1998) suggested that the surface deformation limits may extend from

50m to more than 250 metres away from the extent of large scale surface cracking

zone.

Fig. 2.4 Relative frequency of break angles for different rock mass qualities (Laubscher‟s

RMR), in the subsidence craters of underground mines by caving methods

(adapted after Flores & Karzulovic, 2002, with permission)

2.4 Factors Governing Subsidence Development

Laubscher (1994) suggested that major geological structures, rock mass

strength, induced stresses and depth of mining are the most important

parameters influencing block caving subsidence development. Flores &

Karzulovic (2002), based on data from ten caving operations ,classified causes of

subsidence by the degree of their influence as summarized in Table 2.1.

0.70

0.65

0.60

0.55

0.50

0.45

0.40

0.35

0.30

0.25

0.20

0.15

0.10

0.05

0.00

0 10 20 30 40 50 60 70 80 90

RMR

70 < RMR 60 < RMR < 70 50 < RMR < 60 40 < RMR < 50

13

Table 2.1 Degree of influence of various factors affecting surface subsidence development suggested by Flores & Karzulovic (2002).

Degree of influence on surface subsidence

High Moderate

Geological Structures

Rock mass quality

Block height

Draw rate

Draw management

Water conditions

Footprint geometry

Caving initiation

Mining sequence

Undercutting management

According to Brown (2003) there are a number of features of the orebody and the

local geology and topography which can influence subsidence development

including the:

dip of the orebody;

plan shape of the orebody;

depth of mining and the associated in situ stress field;

strengths of the caving rock mass and of the rocks and soils closer to the

surface;

nature of the slope of the ground surface;

presence of major geological features such as faults and dikes

intersecting the orebody and/or cap rock;

prior surface mining;

accumulation of caved or failed rock, or the placement of fill, in a pre-

existing or a newly formed crater; and

presence of nearby underground excavations.

It should be emphasized that the published literature sources, surveyed as part

of this research, focus on the importance of geologic structure on subsidence

development and provide minimal or no elaboration on the effect of other factors.

Crane (1929) carried out measurements of caving at a number of iron ore mines

in Michigan. He suggested that rock breaks according to a systematic

arrangement of planes of weakness (joints) with slight irregularities due to

breaking between joints. In the absence of faults and dykes, joint dip governs

14

the angle of break. The angle of break for a mine should be equal to the dip of

the most prominent joint, where prominence is a measure of number of

observations, joint persistence and character of the joint surface. Wilson (1958)

studied geological factors influencing block caving at San Manuel mine, USA

where it was noted that that there is close agreement between trends of

subsidence deformations and local fracture systems. Parker (1978) indicated

that in weak rocks there may be no significant geologic structure, hence the

reported cave angles are usually consistent and can be predicted with

reasonable confidence. In stronger rocks, however, the angle of break is usually

controlled by geological structures. A well defined fault plane, which is parallel to

a mining face and steep to moderately inclined, will result in a cave which

propagates to surface fairly rapidly and is defined on the surface by the trace of

the fault plane. If the predominant joints and faults are roughly perpendicular to

the mining front, caving may be inhibited and negative break angles may occur.

As noted by Stacey & Swart (2001) and van As (2003) in most cases when a

mining face encounters a significant discontinuity, such as a fault, with moderate

to steep dip, movement will occur on the fault regardless of the cave angle

through the intact rock. A stepped topographical crack will appear where the

fault daylights at surface. If mining is only on the hangingwall side of the fault

there will only be surface movements on the one side. If the fault dip is steeper

than the cave angle the extent of surface subsidence will be reduced.

Conversely, if the fault dip is less than the cave angle the extent of surface

subsidence will be increased, as illustrated in Fig. 2.5. The intersection of major

geological structures in a subsidence crater wall may define a wedge, within which

the rock mass has greater freedom to deform. The initiation of localised failure and

its progression will be facilitated within this zone of greater freedom of movement,

allowing the ultimate development of crater wall failure.

According to van As (2003) many observations of the influence of discontinuities

have been made; however, only a modest amount of research work has been

carried out to qualify and quantify the influence on surface subsidence

development. Based on the analysis of subsidence in coal mines Hellewell

15

(1988) asserted that quantifying the effects of discontinuities is complicated by

the fact that many features have not reacted adversely when subjected to

subsidence and the results of scientific investigations are in some instances

contradictory. Similar reasons explain the apparent lack of quantitative data from

block caving operations.

Fig. 2.5 Beneficial and detrimental effects of major weakness planes

(adapted after Stacey, 2007, with permission)

2.5 A Block Caving Subsidence Analysis Toolbox

2.5.1 Empirical Methods

Empirical methods are traditionally used in rock engineering and are based on a

synthesis of past observations, usually in similar settings, to describe the tentative

response trends associated with the studied phenomenon. Empirically based

block caving subsidence estimates include “rules of thumb” and experience based

design charts linking angle of break, rock mass rating and other parameters.

One example of an empirical approach is given in “The Hard Rock Miner‟s

Handbook - Rules of Thumb” (McIntosh Engineering, 2003) where it is stated that

disturbed zone

UNIFORM ROCK MASS

EFFECT OF STEEPLY DIPPING FAULT

EFFECT OF SHALLOW DIPPING FAULT

fault

fault

disturbed zone

subsidence crater

subsidence crater

subsidence crater

16

the design of a block cave mine should assume a potential subsidence zone of 45

degrees from the bottom of the lowest mining level. Although it is unlikely that actual

subsidence will extend to this limit, there is a high probability that tension cracking

will result in damage to underground structures (such as a shaft) developed within

this zone, no permanent surface structures should be placed within this limit

(Hartman, 1992). Clearly such a “rule of thumb” may be rather conservative, non-

specific and provide only a crude estimate of potential subsidence.

The most commonly used empirical method in cave mining for estimating

subsidence damage limits is the Laubscher method (Laubscher, 2000). Laubscher

proposed a design chart (see Fig. 2.6) that relates the predicted cave angle (angle

of break) to the MRMR (Laubscher‟s Mining Rock Mass Rating), density of the

caved rock, height of the caved rock and mine geometry (minimum and maximum

span of a footprint).

Fig. 2.6 Empirical chart relating MRMR and cave (break) angle

(after Laubscher, 2000)

Flores & Karzulovic (2004) noted that this method does not take into account the

effect of geological features like faults which may influence the dip of the cave

17

angle, nor does it consider the apparent difficulty in determining density of the

caved rock. Overall, the Laubscher chart is a useful tool for preliminary estimates

of the angle of break, although it is too general to be relied solely upon in design.

The estimated break angles should be adjusted to account for the effect of

geological structures. This however is not a trivial exercise and requires sound

engineering judgement.

2.5.2 Limit Equilibrium Techniques

The concept of limit equilibrium has been widely applied in the analysis of soil

and rock engineering problems and is in essence based on a series of analytical

solutions aimed at the evaluation of rigid body stability above a defined failure

surface.

The initial limit equilibrium model for the analysis of tensile fracturing limits

associated with the progressive sub-level caving of an inclined orebody was

developed by Hoek (1974) for the analysis of subsidence at the Grängesberg mine

in Sweden. Hoek (1974) proposed a conceptual mechanism of hanging wall

failure during progressing downhole mining as illustrated in Fig. 2.7.

Fig. 2.7 Progressive hanging wall failure sequence with increasing depth of mining (a) mining from outcrop; (b) failure of overhanging wedge; (c) formation of steep face; (d) development of tension crack and failure surface; (e) development of second tension crack and failure surface. (adapted after Hoek, 1974, with permission)

orebody

ground surface

(a) (b) (c)

(d) (e)

18

It was assumed that at each stage of vertical retreat a tension crack and a failure

surface form in the hanging wall at a critical location determined by the strength

of the rock mass and the imposed stresses. A limit equilibrium solution was

developed to determine the stability of the block of rock isolated by the new

tension crack and failure surface formed at each stage of mining. Using Hoek‟s

analysis it is possible to predict the angle of inclination of the new failure surface,

new tension crack depth and angle of break as the depth of mining increases,

Fig. 2.8. The analysis assumes a flat ground surface and full drainage

throughout the caving mass. Hoek‟s method is applicable to progressive

hangingwall failure only, and requires input of initial subsidence conditions.

H1 Previous mining level depth H2 Current mining level depth Hs Depth to the caved material surface Hc Caved material height z1 Previous tension crack depth z2 New tension crack depth ψ0 Dip of the orebody ψb Break angle ψp1 Inclination of the previous failure plane ψp2 Inclination of the new failure plane φw Friction angle between caved material and

rock wall θ Inclination of the line of action of T Wc Weight of the caved material W Weight of the potentially unstable block T Lateral force due to Wc on the potentially

unstable block Tc Lateral force due to Wc on the footwall γc Unit weight of the caved material γ Unit weight of rock mass c Cohesion and rock mass φ Angle of friction of rock mass

cossin

)sin(cos

)sin(tantan

2

0

022

22

2

ZH

Z

p

p

pb Tension crack from previous failureTension crack from previous failureNew tension crack

Working face

Orebody

Footwall

Caved

material

Fig. 2.8 Idealised model for limit equilibrium analysis of progressive hangingwall caving proposed by Hoek (1974)

Several authors have modified Hoek‟s method to incorporate various additional

parameters and mining geometries. Table 2.2 summarizes the available limit

equilibrium approaches to the analysis of caving induced subsidence developed

after Hoek (1974).

19

Table 2.2 Evolution of limit equilibrium methods of subsidence analysis (modified after Flores & Karzulovic, 2004 with permission)

Author(s) Brief Method Description and Applications

Brown & Ferguson (1979)

Extended Hoek‟s limit equilibrium model to account for a sloping surface and groundwater pressures in the tension crack and on the shear plane. This model was used to evaluate the progressive failure of the hanging wall at Gath‟s mine in Rhodesia.

Kvapil et al. (1989)

Used Hoek‟s limit equilibrium model to include the progressive failure occurring in both hanging wall and footwall in a very steeply dipping orebody. This model was applied at El Teniente mine, in Chile, to evaluate the subsidence generated by underground block and panel caving operations.

Karzulovic (1990)

Used Brown and Ferguson‟s limit equilibrium model to predict discontinuous subsidence associated with block caving at Rio Blanco mine in Chile. This model was developed to evaluate subsidence in a vertical orebody.

Herdocia (1991)

Proposed a simplified geometrical model for the calculation of geometrical factors affecting the stability of hanging walls in an inclined orebody using a sublevel caving method. This limit equilibrium model was used to evaluate the hanging wall stability at Grängesberg, Kiruna and Malmberget mines, in Sweden.

Lupo (1996)

This model considers the failure of the hanging wall using the limit equilibrium equations derived by Hoek (1974) but considering an active earth pressure coefficient, and the limit equilibrium equations derived by Hoek (1970) for excavated slopes in open pit mines to analyse the footwall. The use of an active earth pressure coefficient is intended to include the effect of the movement of broken rock during draw. This method was applied to the analysis of sublevel caving at the Kiruna mine, in Sweden.

Flores & Karzulovic (2004)

Developed a model for a case of transition from open pit to underground mining by caving methods. Extended Karzulovic (1990) limit equilibrium solution to account for the geometry with an existing open pit. Considered a sub-vertical orebody, sloping ground, influence of surface traction of caved rock and a pore water pressure. Based on a limit equilibrium model and supplemental FLAC modelling a series of design charts relating angle of break, zone of influence and rock mass quality and crater depth were derived.

20

Heslop & Laubscher (1981) indicated that a governing factor in hanging wall

failure is rock structure. The presence of faults may provide preferential shear

failure planes. Persistent discontinuities having similar dip to an orebody may

create a tendency for toppling failure, as illustrated in Fig. 2.9. Woodruff (1966)

postulated that the tension cracks surrounding a caved or subsidence area do

not necessarily represent planes of movement extending from ground surface to

undercut level. It appears that the mechanism of failure behind Hoek‟s (1974)

limit equilibrium approach may not be applicable in all cases. It should be noted

that the predictive capabilities of limit equilibrium techniques are restricted to the

estimation of the angle of break. Overall, even the advanced limit equilibrium

approaches should be treated as very approximate as they do not account for

complex rock structure, in-situ stresses and neglect stress-strain relationships.

Fig. 2.9 Toppling of steeply dipping hangingwall strata (after Brady & Brown, 2004).

van As (2003) suggested that given the significant cost implications of locating

major excavations and infrastructure beyond the influence of the cave subsidence

limits it is well worth the effort of using numerical modelling to ensure that the

empirical or analytical methods are not overly conservative in their predictions.

Similarly Brown (2004) recommended using a combination of empirical, analytical

and numerical methods for subsidence predictions. It was suggested to derive a

preliminary estimate of the angle of break using Laubscher‟s chart and then calibrate

it against observed angles of break in similar mining settings. The estimated angle

of break should then be checked against limit equilibrium approaches. The

21

estimated value of the angle of break can be adjusted to take into account local

geological features and the amount of broken material in the crater. Finally,

numerical methods should be used to confirm the estimate of the angle of break and

to estimate the stresses and displacements induced in the rock mass around the

caved zone.

2.5.3 Numerical Approaches

Numerical methods offer a powerful, sophisticated and flexible framework for the

analysis of engineering systems allowing consideration of complex geometries,

factors and mechanisms unattainable through use of empirical and analytical

techniques. Rapid advances in computing technology over the last two decades

have made numerical methods often routine in rock engineering analysis. Here

Section 2.5.3.1 provides a concise introduction to numerical techniques and

Section 2.5.3.2 discusses block cave subsidence related modelling studies.

2.5.3.1 Numerical Modelling in Rock Engineering

According to Hoek et al. (1991) all numerical methods adopt the approach of

dividing the problem into smaller physical and mathematical components and then

summing their influence to approximate the behaviour of the combined system.

The most common way to compute the series of equations formed during this

process is to assemble them into matrices, which can be solved by a variety of

techniques. This usually requires storage of large systems of matrix equations,

and the technique is known as the “implicit” solution method. The implicit method

is most efficient for solving problems with comparatively simple constitutive laws.

For more complex problems where reformulation of multiple matrices is required,

the implicit technique is less efficient. An alternative method, known as the

“explicit” solution scheme, is based on the assumption that a disturbance at a point

in space is initially felt only by points in its immediate surrounding. With

continuous computational steps the disturbances spreads through the whole

system until equilibrium is reached. This method usually involves solution of the

full dynamic equations of motion, even for problems that are essentially static or

22

quasi-static. The explicit methods do not require the storage of large systems of

equations.

Hoek et al. (1991) classified available numerical methods into two categories,

boundary and domain methods:

In boundary methods only the problem boundaries are defined and

discretized. The boundary element method (BEM), including the

displacement discontinuity method (DDM), is based on this proposition.

In domain methods, the whole modelling domain is divided into a finite

number of sub-regions or elements, as illustrated in Fig. 2.10. Finite

element (FEM), finite difference (FDM) and discrete element (DEM)

methods belong to this category.

Fig. 2.10 Example of problem discretization using FEM (modified after Brady & Brown, 2005, with permission).

Detailed descriptions of these numerical methods may be found in a large

number of textbooks (e.g., Becker, 1992; Zienkiewicz et al., 2005; Davis, 1986;

Jing & Stephansson 2007).

Generally, there are three possible approaches to model rock engineering

problems: Continuum, Discrete, and Hybrid, as illustrated in Fig. 2.11. In the

rock mechanics context the use of BEM, FEM, and FDM methods is generally

based on the assumption that the rock mass behaves as a continuum medium,

23

i.e. it cannot be torn open or broken into pieces. Use of the DEM implies the rock

mass behaves as a discontinuum medium, consisting of a finite number of

interacting bodies (e.g., blocks, particles and etc.). Hybrid approaches attempt to

capitalize on the advantages of the continuum and discontinuum methods by

combining them into a single model, allowing, for instance representation of the

near field excavation area with discrete elements and the use of a continuum to

represent the far-field material (see Fig. 2.11(c)) therefore improving

computational efficiency. It should be noted that hybrid models have not to date

found widespread use in rock engineering with most analyses carried out using

either continuum or discontinuum approaches.

(a) FEM / FDM / BEM (b) DEM

(c) combination of FEM / FDM / BEM and DEM

Fig. 2.11 Various approaches to model rock engineering problems: (a) continuum, (b) discrete and (c) hybrid

The numerical methods and their implementation in the most commonly

employed in rock engineering proprietary numerical codes are summarized in

Table 2.3.

24

Table 2.3 Numerical methods and proprietary codes widely applied in rock engineering

Numeri-cal Method

Modelling Approach

Numerical code Rock Mass Represen-tation

Rock Mass Failure Realization

FDM,

FEM

Co

ntin

uu

m

FLAC 2D/3D

(Itasca, 2007);

Phase2

(RocScience Ltd., 2007)

Continuum medium

Flexural deformations, plastic yield

BEM

Map3D

(Mine Modelling Pty Ltd, 2007)

NFOLD

(Golder Associates, 1989)

MULSIM

(Zipf, 1992)

Elastic deformations

DEM

Dis

co

ntin

uu

m UDEC/3DEC

(Itasca, 2007)

Assembly of

deformable or rigid blocks

Blocks movements

and/or blocks deformations

PFC2D/3D

(Itasca, 2007)

Assembly of rigid bonded particles

Bond breakage,

particle movements

Further information on the numerical modelling techniques applied in rock

engineering can be found in Cividini (1993), a recent review by Jing (2003) and the

respective manuals for the proprietary codes listed in Table 2.3. It should be

emphasized that the choice of the suitable modelling technique should always be

problem specific, and in some cases, may require the use of a combination of

different methods.

2.5.3.2 Numerical Modelling of Caving Induced Subsidence

A comprehensive literature survey reveals that there are relatively few published

accounts describing the modelling of surface subsidence associated with caving

mining. The most important of these are summarized in Table 2.4.

Singh et al. (1993) used the continuum finite difference code FLAC to simulate

progressive development of fractures in the hanging wall and footwall with

25

increase in mining depth in sublevel caving. The analysis was carried out at

Rajpura Dariba (India) and Kiruna (Sweden) mines. The modelling results were

found to be in reasonable agreement with field measurements.

Table 2.4 Numerical studies of caving induced surface subsidence.

Author(s) Code Type of analysis

Singh et al. (1993) FLAC Site specific: Rajpura Dariba and Kiruna

mines

Karzulovic et al. (1999) FLAC Site specific: El Teniente mine

reported by van As (2003) FLAC 3D Site specific: Northparkes mine

Cavieres et al. (2003) 3DEC Site specific: El Teniente mine

Flores & Karzulovic (2004) FLAC & FLAC 3D

Conceptual

Gilbride et al. (2005) PFC 3D Site specific: Questa mine

Brummer et al. (2006) 3DEC Site specific: Palabora mine

Itasca Ltd.

reported by Elmo et al. (2007a)

FLAC 3D Site specific: San Manuel mine

Villegas & Nordlund (2008a,b) Phase2,

PFC 2D

Site specific: Kiruna mine

Karzulovic et al. (1999) performed a study using Karzulovic‟s (1990) limit

equilibrium model to predict the evolution of the subsidence crater at El Teniente

mine (Chile), and conducted numerical modelling using FLAC to assess the

extent of the zone of influence. The angle of break calculated using the limit

equilibrium approach was adjusted to take into account major geological

structures. The numerical models were calibrated against field observations to

define the limits of the influence zone.

van As (2003) reported that subsidence modelling of the Northparkes (Australia),

Lift 1 block cave was undertaken using FLAC 3D in an attempt to define the

extent of the cave deformation and subsidence limits (for both underground and

surface), and to quantify the increase in the abutment stresses subsequent to

cave break-through. The results of the modelling proved far more reliable and

“closer to reality” than those derived using empirical methods. van As (2003) also

26

postulated that caution must be exercised when using numerical models to ensure

that a reliable geological model forms the framework of the numerical model.

Cavieres et al. (2003) employed the 3DEC code to carry out analysis of the

evolution of fracturing limits in Braden Pipe associated with caving mining at El

Teniente mine. The mine scale model was built and calibrated against observed

subsidence damage, and then subsequently used to make forward predictions. It

was concluded that the main mechanism governing the growth of the fracturing

limit is a loss of confinement of the Braden Pipe‟s wall resulting from mining at its

perimeter. The authors found the contours of total strain to be good indicators of

subsidence limits. Based on the modelling results a mine subsidence monitoring

program, focussing on strain measurements was recommended.

As a part of Stage II of the International Caving Study, Flores & Karzulovic (2004)

conducted conceptual FLAC/FLAC3D modelling of the surface subsidence during

block caving, for the case with an existing open pit, varying rock mass strength,

open pit depth and undercut level depth. Based on their modelling results

combined with limit equilibrium analysis, a series of design charts were

developed correlating angle of break and zone of influence of caving with

undercut level depth and crater depth for rock with varying rock mass quality.

Fig. 2.12 shows an example of such a chart. It should be noted that in their analysis

Flores & Karzulovic (2004) did not account for the presence of geological structures.

Moreover, the validity of these charts is yet to be confirmed by mining experience.

Gilbride et al. (2005) conducted a three-dimensional study of surface subsidence

at the Questa mine (USA) using PFC3D. The rock mass was simulated as an

assembly of bonded spheres with diameters of 13 to 20 metres. The authors

stated that the true advantage of a spherical particle code (PFC3D) for modelling

surface subsidence in block caving settings lies in it‟s ability to simulate large-

displacement mass flow simultaneous with elastic and small-strain, inelastic

deformation. Simulated rock mass behaviour was found to be reasonably

realistic and subsidence trends were found to be in good agreement with surface

deformation measurements at the site. The authors noted that the assumption of

27

the large diameter spheres prevented some potentially influential smaller-scale

deformation mechanisms from developing in the cave and near the surface. It

was emphasized that it remains a challenge to achieve both computational

efficiency and reasonable simulated behaviour with PFC3D for mine scale

subsidence problems. In this context a spherical particle size that is “too small”

has yet to be attained.

45 50 55 60 65 70 75 80 85 90

Angle of Break, b (degrees)

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

1700

UC

L

De

pth

, H

T

(me

ters

)

Rock Mass Geotechnical Quality

Poor to Fair

Fair to Good

Good to Very Good

b

HT

45 50 55 60 65 70 75 80 85 90

Angle of Break, b (degrees)

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

1700

UC

L

De

pth

, H

T

(me

ters

)

Rock Mass Geotechnical Quality

Poor to Fair

Fair to Good

Good to Very Good

b

HT

b

HT

Fig. 2.12 Design chart for estimation the angle of break in a transition from open pit to underground mining by block/panel caving (adapted after Flores & Karzulovic, 2004 with permission)

Brummer et al. (2006) carried out 3-dimensional 3DEC analysis of open pit wall

failure mechanisms associated with block caving at the Palabora mine (South

Africa). This study was instigated by a massive failure at the North wall of the

28

Palabora mine during block caving operations. Mine scale 3DEC modelling

incorporating major geological structures (faults and joint sets) showed that

observed movements were most likely caused by the fact that pervasive joint

sets may form wedges that daylight into the cave region below the pit. The draw

of the ore into the cave zone undermines the pit wall, and appears to have a

direct control on the movements.

As reported by Elmo et al. (2007a), Itasca Ltd. carried out back analyses of

subsidence due to caving at San Manuel mine (USA) using FLAC3D. Being a

continuum code, FLAC3D, cannot explicitly model discontinuous behaviour. It

was necessary to incorporate the effects of jointing for the model to be

representative. Based on Clark (2006) the Equivalent Rockmass Model (ERM)

was proposed. To account for joint fabric, randomly oriented ubiquitous joint

planes were distributed through every zone in the model according to the

mapping data. This allows for the larger scale behaviour to be affected by small

scale effects. Initial simulations based on FLAC3D mine scale model and the

ERM concept have yielded promising results with the subsidence profile and

breakthrough matching observations reasonably well.

Villegas & Nordlund (2008a) carried out numerical analysis of hanging wall failure

at Kiruna mine using Phase2. The caving process was simulated by adding

voids moving upwards from the extraction level and changing the properties of

the material when the void was filled. Based on the estimated failure location on

the ground surface, the break angle and the limit angle were calculated for

different mining levels. The results indicated that the break angle and the limit

angle are almost constant for deeper mining levels. However, the limit angle

differs between sections with different rock mass strength. Moreover, the break

angle could be altered by large geological structures. It should be emphasized

that the Phase2 model exhibited excessive tensile deformations at the surface,

particularly in far-field. Villegas & Nordlund (2008b) also analyzed subsidence

deformations at Kiruna mine using PFC2D. The modelling indicated that

although tension cracks develop at the surface the primary failure mechanism in

the hangingwall is shear. In addition, it was shown that the caved rock and the

29

backfill in the pit provide support to the footwall and hangingwall therefore

reducing the magnitude and extent of surface subsidence.

Overall the following can be noted with respect to the previous subsidence

modelling attempts:

the majority of subsidence modelling studies have attempted to simulate

mine scale geometries in 3D and consequently were based on fairly

coarse models;

all the modelling studies, with the exception of that by Flores & Karzulovic

(2004), focused on back analysis or predictive modelling of particular mine

sites.

2.6 Summary

A comprehensive literature survey has shown that our knowledge of rock mass

behaviour leading to surface subsidence in block caving settings is rather

tentative and primarily founded on empirical, mostly qualitative, observations.

This is perhaps not surprising given the scale of the block caving problem, the

complexity of rock mass response and the multitude of factors affecting

subsidence. The literature focuses on the importance of the effect of geological

discontinuities in subsidence development, stopping short of elaborating on the

effect of other factors.

Available methods of subsidence analysis include empirical, analytical and numerical

approaches. The empirical methods are not particularly reliable. The analytical

approaches are restrictive, being based on Hoek‟s (1974) assumed failure

mechanism, and are able to provide only estimates for the angle of break. The

numerical approaches being inherently more flexible and sophisticated offer an

opportunity to improve our understanding of block caving subsidence phenomena and

increased accuracy of subsidence predictions. However, previous modelling studies

were largely oriented towards providing subsidence predictions for a particular site.

The modelling study by Flores & Karzulovic (2004) was the first attempt after

Laubscher (2000) to provide non-site specific guidance for subsidence analysis. It

30

should be noted that their modelling was limited to the case with an open pit and no

consideration was given to the effects of significant factors including rock structure. It

appears that to date no comprehensive attempt has been made to evaluate the

general principles characterizing surface subsidence development in block caving

settings and evaluate the predominant factors governing subsidence phenomena.

31

CHAPTER 3: RESEARCH METHODOLOGY AND THEORY

3.1 Introduction

This chapter discusses the available modelling approaches for simulation of

block caving surface subsidence phenomena and introduces the finite/discrete

element method with fracture propagation code used in the current analysis. An

overview of the fundamentals of fracture mechanics is provided as well as an

outline of the implementation of this approach in the proprietary code ELFEN.

The advantages of this type of geomechanical modelling are highlighted and its

integration with Discrete Fracture Networks (DFN) is discussed. Finally the

proposed modelling methodology is outlined.

3.2 Modelling Approach Selection

3.2.1 Analysis of Available Modelling Approaches

Block caving subsidence is a product of a complex rock mass response to

caving. This response comprises massive failure of the rock mass driven by

brittle fracture, both in tension and compression, along existing discontinuities

and through intact rock bridges. Moreover, block caving subsidence

development almost invariably involves complex kinematic mechanisms.

As discussed in Section 2.5.3.1 traditional rock mechanics modelling techniques

include a variety of continuum and discontinuum methods. In the FDM and FEM

based continuum approaches the effect of brittle fracturing can be accounted for

implicitly by use of plasticity models or a damage mechanics failure criterion

(Hajiabdolmajid et al., 2001 and Fang & Harrison, 2002). The BEM based

continuum approach allows, for pre-existing flaws, explicit simulation of rock

fracture initiation and growth under mode I (tensile), II (shear) and mixed fracture

modes. Among various techniques to simulate fracture propagation, the

32

displacement discontinuity method (Crouch & Starfield, 1983) is the most efficient.

Several researchers, including Scavia (1990, 1995), Scavia & Castelli (1996) and

Muller & Martel (2000) have applied BEM based fracture codes to analyse failure

initiation in slopes. Although as noted by Jing (2003), to date, due to the

computational difficulties involved in the analysis of BEM fracture growth, the

majority of studies were often performed considering a small number of isolated,

non-intersecting fractures, frequently laboratory scale 2-D models. These models

involved local failure mechanisms, such as borehole breakout and step-path

fracture propagation (see for instance works by Backers et al., 2006, Yan, 2008).

According to Choi (1992), despite many adaptations, continuum models are not

suitable for modelling a rock mass where large scale sliding, separation, and

rotation will occur along discontinuities. It should be recognized that even

advanced continuum techniques are unable to capture the true failure kinematics.

In DEM based discontinuum approaches the effect of brittle fracturing can be

simulated indirectly through particle assembly analysis (Potyondy & Cundall, 2004)

and a sliding joint model (Pierce et al., 2007) using PFC 2D/3D. One drawback of

this approach is that particle bond breakage or a sliding joint model are not based on

fundamental fracture mechanics but governed by simple bonding models. An

alternative DEM approach is based on the UDEC Voronoi tessellation algorithm

which divides rock mass into polygonal blocks, allowing simulation of crack

propagation and fracturing occurring when strength between blocks is exceeded.

Fairhurst (2006) and Christianson et al. (2006) applied this approach for analysis of

lab and slope scale problems. Similar to the PFC based approaches these modelling

techniques did not consider fracture mechanics principles. Voronoi analysis trials

were carried out in the current research as part of the methodology selection process

and demonstrated the very low efficiency of the Voronoi mesh generator, i.e. a

geometry of medium complexity could take up to several hours to mesh. Kemeny

(2005) using both fracture mechanics and the UDEC discontinuum approach

developed a methodology for time-dependant analysis of rock bridge failure.

Overall, both continuum and discontinuum approaches to rock mass modelling

provide a convenient framework for the analysis of many engineering problems

33

however they are not always applicable to highly complex engineering problems

such as block caving subsidence due to the above limitations. It appears that

realistic simulation of the subsidence phenomena necessitates consideration of

fracture mechanics principles for brittle fracturing simulation and a blend of

continuum and discontinuum approaches to capture the complex failure

mechanisms.

3.2.2 Fracture Mechanics Based Hybrid Continuum/Discontinuum Approach

In the current study a state-of-the-art hybrid continuum-discontinuum approach

based on the finite/discrete element method (Munjiza et al., 1995) and incorporating

fracture mechanics principles is adopted. In the combined finite-discrete element

method the finite element-based analysis of continua is merged with discrete

element-based transient dynamics, contact detection and contact interaction

solutions (Munjiza, 2004). Use of fracture mechanics principles in combination with

the finite-discrete element method allows the caving process to be simulated in a

physically realistic manner. Rock mass failure is realized through a brittle fracture

driven continuum to discontinuum transition with the development of new fractures

and discrete blocks, and full consideration of the failure kinematics. Table 3.1

summarizes the hybrid continuum-discontinuum with fracture approach.

Table 3.1 Hybrid continuum-discontinuum with fracture modelling approach

Modelling Approach

Numerical Method

Rock Mass Representation

Rock Mass Failure Realization

Fract. Mech. based Hybrid Continuum-Discontinuum

FEM/DEM Continuous medium

Degradation of a continuum into discrete deformable blocks through fracturing and fragmentation

Intensive research carried over the last 15 years has facilitated major advances in

FEM/DEM theory and led to the development of several codes including Y (Munjiza

et al., 1999), VGW (Munjiza & Latham, 2004) and ELFEN (Rockfield Software Ltd.,

2006). So far ELFEN is the only fully featured commercially available code and

therefore was adopted for the current study. ELFEN is a multipurpose FEM/DEM

software package that utilizes a variety of constitutive criteria and is capable of both

34

implicit and explicit analyses in 2-D and 3-D space. It has the capability to simulate

continuum materials, jointed media and particle flow behaviour. The current study

uses only the hybrid FEM/DEM features of the code.

3.3 Fundamentals of Fracture Mechanics

Before introducing the ELFEN code it is important to outline the relevant basic

elements of fracture mechanics. This discipline deals with crack propagation and

provides a quantitative description of the transformation of an intact structural

component into a fractured medium by crack growth.

In the fracture mechanics of a solid three basic crack loading modes (or their

combinations) are assumed (see Fig. 3.1):

Mode I: opening or tensile mode (the crack faces are pulled apart);

Mode II: sliding or in-plane shear (the crack surfaces slide over each other);

Mode III: tearing or anti-plane shear (the crack surfaces move parallel to

the leading edge of the crack and relative to each other).

Mode I Mode II Mode III

Fig. 3.1 Fracture mechanics basic crack tip loading modes (based on Whittaker et al., 1992).

There is some debate in the literature as to which mode of fracturing is predominant

in specific rock mechanics problems. Whittaker et al. (1992) concluded that the

majority of fracture problems in rock mechanics involve a combination of modes I-II.

Liu (2003) indicated that in mixed I-II modes and even in pure mode II, tensile

failure is still the overwhelming failure mode. Scholz (2002) states that it is not

possible for a shear crack in an isotropic elastic medium to grow in its own plane.

Instead, the propagation of a shear crack due to 1 (major principal stress) occurs

35

by the generation of mode I cracks parallel to 1. In other words, what appears to

be shear fracturing on macroscopic level is realized by formation of an echelon

tensile crack system on a microscopic level, with increasing loading these tensile

cracks link up and form a shear plane.

The fracture insertion algorithm in the current ELFEN code is based on mode I or

tensile fracturing (development of a mode II fracture capability is ongoing).

Considering the above discussion and the notion by Singh et al. (1993) that in

caving mining a tensile mode of fracturing is predominant; the assumption of purely

tensile failure for the block caving subsidence analysis appears to be reasonable.

Griffith (1921) established a relationship between fracture stress and the crack size

that led him to state that a crack in a material will propagate if the total energy of the

system is lowered with crack propagation. That is, if the change in elastic strain

energy due to crack extension is larger than the energy required to create new crack

surfaces then crack propagation will occur. Griffith`s theory was developed for

perfectly brittle materials. Irwin (1957) extended the theory for quasi-brittle

materials. He postulated that the energy due to plastic deformation must be added

to the surface energy associated with the creation of new crack surfaces. He

recognized that for quasi-brittle materials, the surface energy term is often negligible

compared to the energy associated with plastic deformation. Furthermore, he

defined a quantity G, the strain energy release rate or "crack driving force," which is

the total energy absorbed during cracking per unit increase in crack length and per

unit thickness. Irwin further showed that the energy approach is equivalent to the

stress intensity approach and that crack propagation occurs when a critical strain

energy release rate G (or in terms of a critical stress intensity, KC) is achieved.

Whittaker et al. (1992) postulated that a fundamental feature of rock fracture

mechanics lies in its ability to establish a relationship between rock fracture strength

and the geometry of cracks or between the cracks and the fracture toughness or

critical stress intensity, KC. Proposed by Irwin (1957), this is the most fundamental

parameter of fracture mechanics and is used to describe the resistance of a crack to

propagation. The fracture toughness represents the extreme value of the stress

36

intensity factor which is a measure of stress intensity in an elastic field. The fracture

toughness can be considered as the limiting value of stress intensity just as the yield

stress might be considered the limiting value of applied stress.

According to the fracture modes described earlier, fracture toughness may be either

mode I (KIC), mode II (KIIC) or mode III (KIIIC), or any mixed mode fracture toughness.

Intrinsic interrelationships exist between the fracture parameters of different fracture

modes. Fracture toughness for a particular rock type can be established through

laboratory testing adopting ISRM suggested methods (ISRM, 1988).

For the Mode I fracture initiation the critical strain release (fracture) energy and the

critical stress intensity factor (fracture toughness) are related according to the

following relationship:

GIC = KIC 2/E (3.1)

where E is Young‟s modulus of the solid.

In ELFEN, fracture propagation is controlled by this criteria and the fracture

energy G (GIC) is one of the input parameters.

Table 3.2 shows fracture mechanics parameters for selected hard to soft rocks.

Further examples can be found in Atkinson (1987) and Whittaker et al. (1992).

Table 3.2 Fracture toughness and fracture energy values for various rock types (based on Scholz, 2002)

Rock type Fracture toughness (MPa√m)

Fracture energy (Jm-2)

Black gabbro 2.88 82

Westerly granite 1.74 56

Solnhofen limestone 1.01 19.7

3.4 Implementation of the Hybrid Continuum-Discontinuum with Fracture Approach in the ELFEN Code

A comprehensive discussion of the finite/discrete element method and its

implementation in the ELFEN code can be found in Munjiza et al. (1995), Yu

37

(1999), Klerck (2000), Munjiza (2004) and Owen et al. (2004a,b). Here only salient

features of the code relevant to the current study are introduced.

3.4.1 Solution Procedure for Continuum to Discontinuum Transition

According to Owen & Feng (2001), problems involving continuum to discontinuous

transition are often characterized by the following:

they are highly dynamic with rapidly changing domain configurations;

sufficient mesh discretization is required;

multi-physics phenomena are involved;

the domination of contact/impact behaviour gives rise to a very strong

non-linear system response.

These factors dictate that there is no alternative to employing time integration

schemes of an explicit nature to numerically simulate such problems.

The solution procedure at each computational time step involves the following steps:

1. Finite element and fracture handling:

computation of internal forces of the mesh;

evaluation of material failure criterion;

creation of new cracks if any;

global adaptive re-meshing if necessary.

2. Contact/interaction detection:

spatial search: detection of potential contact/interaction pairs among

discrete objects;

interaction resolution: determination of actual interaction pairs through

local resolution of the kinematic relationship between (potential) interaction

pairs;

interaction forces: computation of interaction forces between actual

interaction pairs by using appropriate interaction laws.

3. Global solution:

computation of velocities and displacements for all nodes.

38

4. Configuration update:

update of coordinates of all finite element nodes and positions of all

discrete objects.

3.4.2 Constitutive Models for Rock Material

The simulation of fracturing, damage and associated softening in ELFEN is

achieved by employing a fracture energy approach controlled by a specified

constitutive fracture criterion. There are two main constitutive fracture models

implemented in the code:

Rankine rotating crack model

Mohr-Coulomb model with a Rankine cut-off

In both constitutive models, fracturing is associated with extensional strain and

thus occurs parallel to the localized loading direction.

According to Klerck (2000) for the Rankine rotating crack model failure occurs

according to the following principles:

a failure threshold is a function of the material tensile strength;

prior to reaching the failure threshold the material is considered to be

homogeneous (i.e. without any faults or defects), and to be linearly elastic;

after violation of the failure threshold or yielding condition, material

damage is initiated (the yield surface is shown in Fig. 3.2(a)).

the failure process is completed once the material strength is totally lost.

At complete failure it is assumed that a physical crack is created through

the material point;

stress softening behaviour is a function of the fracture energy release rate Gf

(see Fig. 3.2(b))

The Mohr Coulomb with Rankine cut-off criteria is a more sophisticated model

that is able to consider material failure both in tension and compression. As

indicated by Klerck et al. (2004) this model is based on the assumption that

quasi-brittle fracture is extensional in nature, i.e. any phenomenological yield

surface is divided into regions in which extensional failure can be modelled

39

directly, as in the case of tensile stress fields and indirectly, as in the case of

compressive stress fields (Klerck et al., 2004).

For degradation and subsequent discrete fracturing of the material in

compression the model employs the Mohr-Coulomb failure criterion in the form of

a softening, isotropic, non-associated elasto-plasticity model (Fig. 3.3).

(a) (b)

Fig. 3.2 Rankine Rotating Crack model: (a) yield surface and (b) softening curve (adapted from ELFEN User manual; Rockfield, 2005, with permission).

Fig. 3.3 Yield surface for the conventional Mohr Coulomb model (adapted from ELFEN User manual, Rockfield, 2005, with permission).

40

The Mohr-Coulomb yield surface in tension cannot reasonably represent the

physically observed plastic flow directions normal to the mutually orthogonal

principal tensile planes. To improve the tensile description, a three-dimensional

rotating crack model is coupled with the Mohr-Coulomb yield surface. According

to Klerck (2000), only the mutually orthogonal tensile planes of the isotropic

Rankine yield surface are able to recover the correct plastic flow directions in

tension. Thus as an approximation to the anisotropic softening response of

physical quasi-brittle materials, the isotropic non-hardening Rankine tensile cut-

off emerges as the most feasible tensile cut-off formulation. Fig. 3.4 shows the

conventional Mohr Coulomb tensile yield surface in a 3D space (Fig. 3.4a),

together with the Mohr Coulomb tensile yield surface with Rankine tensile corner

(Fig. 3.4b).

Fig. 3.4 Yield surfaces for (a) Mohr Coulomb and (b) Mohr Coulomb with Rankine tensile cut-off criteria (adapted from ELFEN User manual with permission, Rockfield, 2005).

According to Klerck (2000) fracturing due to dilation is accommodated by

introducing an explicit coupling between the inelastic strain accrued by the Mohr-

Coulomb yield surface and the anisotropic degradation of the mutually orthogonal

tensile yield surfaces of the rotating crack model. An explicit coupling between

compressive stress induced extensional strain and tensile strength degradation

permits the realisation of discrete fracturing in purely compressive stress fields.

The Rankine tensile corner introduces additional yield criteria defined by:

41

i – ft = 0; i = 1,2,3 (3.2)

where i refers to each principal stress and ft is tensile strength.

Although at present no explicit softening law is included for the tensile strength,

indirect softening does result from the degradation of cohesion according to the

following criteria:

t c 1 sin cos (3.3)

This ensures that a compressive normal stress always exists on the failure shear

plane.

According to Klerck (2000), the isotropic non-hardening Rankine tensile cut-off for

the isotropic Mohr-Coulomb yield surface constitutes a means of incorporating the

return-mappings needed for the implementation of the compressive fracture model.

Klerck et al. (2004) demonstrated that the combined Mohr-Coulomb with Rankine

tensile cut-off model is able to effectively simulate realistic fracture propagation in

rock under both tensile and compressive stress fields. This model is employed in

the current study.

The following input parameters are required for Mohr-Coulomb model with a

Rankine cut-off:

Young‟s modulus, E

Poisson‟s ratio,

Density, ρ

Cohesion, c

Friction angle,

Dilatancy angle,

Tensile strength, t

Fracture energy, Gf

3.4.3 Continuum Degradation through Fracturing

One of the critical issues of continuum to discontinuum transition is how to

convert the continuous finite element mesh to one with discontinuous cracks.

42

The fracture algorithm employed in ELFEN inserts physical fractures or cracks

into a finite element mesh such that the initial continuum is gradually degraded

into discrete bodies. At some point in the analysis when the strength limit has

been reached, the adopted constitutive model predicts the formation of a failure

band within a single element. Anisotropic damage evolution is initiated by

degrading the elastic modulus, E, in the direction of the major principal stress

invariant. As described by Owen et al. (2004a) a special damage indicator Fk

defined as a ratio of the inelastic fracturing strain f and the critical fracturing

strain fc is employed for damage evaluation:

Fkf f

c k (3.4)

where k is a Gauss point of an element in the model and the critical fracturing

strain is given by

fc 2Gf / hcft (3.5)

where Gf is fracture energy, hc is crack band width, and ft is tensile strength

The load carrying capacity across a failure band decreases to zero as damage

increases until eventually the energy needed to form a discrete fracture is released

and the damage indicator reaches unity. At this point the topology of the mesh is

updated, initially leading to fracture propagation within a continuum and eventually

resulting in the formation of discrete elements as the rock fragments are formed.

As described by Owen et al. (2004a), a discrete crack is introduced when the

tensile strength in a principal stress direction reaches zero and is orientated

orthogonal to this direction. The crack is then inserted along the failure plane.

The failure plane is defined in terms of a weighted average of the maximum

failure strain directions of all elements connected to the node. There are two

options for crack insertion: intra-element and inter-element, as shown in Fig. 3.5.

If a crack is inserted exactly through the failure plane (Fig. 3.5b), some ill-shaped

elements may be generated and local re-meshing is then needed to eliminate

them. Alternatively, the crack is allowed to propagate through the most closely

43

aligned element boundary (Fig. 3.5c). In this way, new elements are not created

and the updating procedure is simplified. However, this approach necessitates a

very fine mesh discretization around the potential fracture area.

Fig. 3.5 Crack insertion in ELFEN (a) weighted average nodal failure direction; (b) intra-element fracture description; (c) the inter-element fracture description. (adapted after Yu, 1999 with permission).

It should be noted that preliminary ELFEN modelling trials carried out as part of the

current study showed that use of the intra-element option was prohibitive due to

numerical instability leading to termination of computations. Therefore, all modelling

analyses undertaken during this study are based on inter-element fracture insertion

and use the finest mesh discretization allowed by the available computing

capabilities.

3.4.4 Contacts Interaction Handling

Crack insertion is followed by application of contact conditions on the crack

surfaces. In ELFEN the interaction of contact surfaces is governed by the

penalty method. Surface penetration that violates the impenetrability constraint

invokes normal penalty (contact) forces Pn that prompt surface separation.

Similarly, tangential penalty forces Pt are invoked by the relative tangential

displacement between contacting surface entities. Normal and tangential

penalties have a similar meaning to the normal (kn) and tangential (ks) stiffness

employed in DEM modelling, as shown in Fig. 3.6. Using the procedure

proposed by Hudson & Harrison (1997), Elmo (2006) back-calculated normal

stiffness values for a series of pillar models containing a single set of horizontally

Failure plane

Failed nodal point

n

44

spaced discontinuities and found a ratio of kn / Pn less than or equal to 1.11. It

was suggested that these parameters can be effectively considered as being

equivalent in magnitude.

Fig. 3.6 Comparison of contacts interaction handling in DEM and FEM/DEM methods (a) meaning of normal and shear stiffnesses for a block containing a single discontinuity (based on Bandis, 1993); (b) penalty contacting couple in ELFEN as an equivalent spring system (based on Klerck, 2000) – adapted after Elmo (2006), with permission

ELFEN uses a Mohr-Coulomb joint slip model to simulate shear failure along joint

contacts. The contact parameters required by ELFEN are:

Normal penalty coefficient, Pn

Tangential penalty, Pt

Cohesion, c

Friction angle, υ

3.4.5 Applications of ELFEN in Rock Engineering

The FEM/DEM plus fracture methodology used in the ELFEN code has been

extensively tested and validated against controlled laboratory tests (Yu, 1999;

Klerck, 2000, Klerck et al., 2004 and Stefanizzi, 2007). In addition, recent work

by Yan (2008) has illustrated that ELFEN simulations of laboratory scale step-

path failure under axial compression are in good agreement with actual physical

tests and correlate well with modelling results obtained by other codes (Phase2,

UDEC and FRACOD).

Numerous researchers including Coggan et al. (2003), Klerck et al. (2004), Cai

& Kaiser (2004), Stead et al. (2004), Eberhardt et al. (2004), Elmo et al. (2005),

Coggan & Stead (2005), Stead & Coggan (2006), Pine et al. (2007), Stefanizzi et

Normal displacements

Shear displacement

kn ks Aperture

σn

45

al. (2007), Karami & Stead (2008), and Yan (2008) have demonstrated the

capabilities of the ELFEN code for the analysis of a number of rock mechanics

problems of various complexity involving brittle failure. Initial applications of the

code for the analysis of block caving by Rockfield Software Ltd (2003), Esci &

Dutko (2003), Pine et al. (2006), Vyazmensky et al. (2007) and Elmo et al.

(2007b), have provided encouraging results.

3.5 Rock Mass Representation Options in Context of Fracture Mechanics Based FEM/DEM Modelling

In the context of finite/discrete element modelling there are three possible

approaches to the representation of the rock mass:

Equivalent continuum;

Discrete fracture network; and

Mixed discrete fracture network/equivalent continuum approach.

In the Equivalent continuum approach, employing continuum modelling techniques,

the jointed rock mass system is represented as an equivalent continuum by means

of reducing intact rock properties to account for the presence of discontinuities.

The degree to which the intact rock properties are scaled can be deduced from one

of a number of rock mass classification systems. It should be noted that the

mechanical behaviour of a jointed rock mass is strongly influenced by the presence

of discontinuities which provide kinematic control and in many cases govern the

operative failure mechanisms. In the Equivalent continuum approach, the

kinematic controls resulting from jointing to some degree can be accommodated by

utilizing a constitutive model that allows directional strength properties.

However, it is suggested that the true kinematic controls of discontinuities cannot

be captured without explicit inclusion of pre-inserted fractures into the models. In

this sense the Discrete Fracture Network approach, where the rock mass is

represented as an assembly of pre-inserted discontinuities and intact rock regions,

is closer to reality. The intact rock properties can be established based on

laboratory tests and the discontinuity characteristics can be determined from field

46

mapping/borehole logging data or stochastic modelling. Fracture representation

must be adequate to capture the realistic behaviour of the specific problem under

investigation. Clearly it is not feasible to consider every single discontinuity within

the rock mass; however the resolution of fractures should be sufficient to capture

salient features of the simulated behaviour.

In some circumstances, such as the simulation of large scale problems, to achieve

reasonable computational efficiency, discontinuities must be placed fairly sparsely.

In this context representation of the rock between fractures as an intact material

may produce an overly stiff response. A mixed approach, where the rock mass is

represented as an assembly of numerically practical spaced discontinuities and

intervening regions with reduced intact properties, is a necessary compromise

between the first two approaches. This allows consideration of the kinematic

effects of discontinuities and adequate computational efficiency. In this approach

the appropriate combination of discrete fracture network/reduced intact rock

properties should be chosen so that the salient features of the simulated response

are captured.

As part of this research Vyazmensky et al. (2007) carried out ELFEN modelling

trials to evaluate the general applicability of the above methods of rock mass

representation to the modelling of block caving induced subsidence. The modelling

based on an equivalent continuum approach demonstrated that use of rock mass

properties derived through available rock mass classification systems produce

results which corresponded reasonably well with some trends observed at actual

block caving mines. Modelling conducted using the Discrete Fracture Network

approach showed that use of intact rock properties in combination with limited

discontinuity input leads to an overly stiff response so that rock mass caving cannot

be adequately captured, thus prohibiting subsidence analysis. An increase in the

number of input discontinuities to allow reasonable simulation of caving behaviour

would require a very fine mesh discretization and lead to excessively long

simulation run-times. Initial modelling, employing the mixed approach using

equivalent continuum properties in combination with pre-inserted discontinuities,

allowed realistic simulation of block caving induced surface subsidence. It was also

47

found that a combination of RMR based properties with an assumed fracture

network resulted in an overly soft response. This indicates that the selection of

equivalent continuum properties for a combined system of pre-inserted fractures

and an equivalent continuum rock mass requires further analysis. Pre-inserted

discontinuities played an important role in subsidence development. In the

equivalent continuum approach tensile cracks must be formed for toppling to occur

whereas in the mixed approach the kinematic conditions for toppling were already

in place, creating preferential directions of failure.

As discussed in Section 2.4, mining experience suggests that block caving

subsidence development is strongly affected by the presence of discontinuities,

and initial FEM/DEM with fracture modelling also supports this observation. It

appears that explicit consideration of discontinuities in the block caving

subsidence models is essential and therefore the mixed discrete fracture

network/equivalent continuum approach to rock mass representation was

adopted for the block caving subsidence analysis.

3.6 Integrated Use of Discrete Fracture Network Models and ELFEN Code

Adequate representation of discontinuities in rock engineering models is essential

for capturing realistic failure mechanisms. In the current study an approach is

taken that integrates the use of the finite element/discrete element code ELFEN

with discrete fracture network (DFN) models capable of providing geologically

sound representation of natural discontinuities. The fundamentals of the DFN

approach can be found in Long et al. (1982) and Dershowitz & Einstein (1987).

3.6.1 DFN Approach to Discontinuity Representation

Accurate characterization of the discontinuities in a jointed rock mass is not a

trivial task due to their inherent three dimensional nature and the frequent

limitations in exposure to spatially isolated surface outcrops, boreholes and

stopes. A number of techniques have been proposed to develop 3D fracture

networks from collected discontinuity data using stochastic modelling. Studies

48

show that, among the different approaches developed to characterize fracture

networks, the discrete fracture network (DFN) model is the most appropriate to

simulate geologically realistic networks (Dershowitz et al., 1996). Initially applied

to the problems of fluid flow transport (Dershowitz, 1992) and hydrocarbon

reservoir modelling (Dershowitz et al., 1998), in recent years the DFN approach

has found wider use in rock engineering analysis (see Staub et al., 2002; Elmo,

2006; Rogers et al., 2006; Rogers et al., 2007 and Elmo et al., 2007b).

DFN models seek to describe the heterogeneous nature of fractured rock

masses by explicitly representing key elements of the fracture system as discrete

objects in space with appropriately defined geometries and properties (Rogers et

al., 2006). By building geologically realistic models that combine the larger

observed deterministic structures with smaller stochastically inferred fractures,

DFN models capture both the geometry and connectivity of the fracture network,

the geometry of the associated intact rock blocks and also the nature of intact

rock bridges connecting fractures (Rogers et al., 2007).

Building DFN models is an iterative procedure that involves multiple random

sampling aiming to build upon limited measured data and eventually replacing it

with a more detailed pseudo-replicate model. Rogers et al. (2007) described the

process of building a DFN model which involves four main stages: data analysis,

conceptual model development, model building and validation. Fig. 3.7 shows

the work flow in this process. Of these stages, validation is particularly important

to ensure a good fit between simulated and collected data. Examples of DFN

model development can be found in Pine et al. (2006) and Elmo (2006). A DFN

model based on this rigorous process is not just a statistical description but an

ordered geologically realistic representation of the distribution, interaction and

geometry of rock mass fractures (Rogers et al., 2007).

49

Geophysics Borehole Data

Well Testing Mapping / Imaging

Geological Model Data Analysis & DFN Inputs

Conceptual Fracture Model

DFN Model Model Validation

Main Data Sources

Validation Loop

Fig. 3.7 DFN model development workflow (modified with permission after Rogers et al., 2007)

3.6.2 Integration of DFN Models into ELFEN

In this thesis the Discrete Fracture Network (DFN) code FracMan (Golder, 2005;

Dershowitz et al., 1998) is employed. FracMan is a convenient tool to generate 3D

stochastical models of fracture networks based on collected discontinuity data; it

allows export of 2D and 3D fracture data into the ELFEN code. Integrated use of

ELFEN and FracMan was first proposed and applied by Elmo et al. (2006) and Pine

et al. (2007). An example of 3D FracMan model and derived 2D trace planes for

ELFEN modelling is given in Fig. 3.8. Elmo (2006) and Rance et al. (2007)

described the methodology for transfer of the FracMan DFN data into the ELFEN

finite element/discrete element model including the following steps:

1. The fracture geometry data are exported from the FracMan system in

Autocad dxf files defining fracture planes within a rock mass on a full three

dimensional basis. These planes may intersect at arbitrary angles and do

not normally traverse the entire region. This information is imported using

a specific modelling interface module in ELFEN in which the joints are

represented as lines for 2D and planar surfaces for 3D situations.

50

2. Imported fracture surfaces are then assigned appropriate interface

properties such as friction coefficient, cohesion, normal and tangential

penalty values.

3. Fracture entities are first constructed independently as a network, accounting

for intersections of lines or surfaces, including the partial intersection of

surfaces in 3D and the intersection with material region boundaries.

4. Once the network has been constructed it is embedded within the

computational solid ELFEN model of the rock mass by inserting fractures

with both sides of the fracture represented as free surfaces. The crack

aperture is normally (as in the current study) assumed closed, but may be

set to a prescribed value.

5. This solid model is then discretized into a finite element mesh employing

triangular (in 2D) and tetrahedral elements (for 3D problems).

Imported discontinuity data may require minor editing to allow discretization.

This may include merging very closely spaced fractures and/or snapping together

fractures terminating in close proximity to each other. Care should always be

taken to ensure that the editing does not introduce significant geomechanical

changes to the rock mass.

Fig. 3.8 Example of a FracMan model (adapted after Elmo, 2006, with permission) (a) FracMan 3D model of a Middleton mine pillar developed based on scanline mapping data; (b) sampling planes used to define the 2D fracture traces models for ELFEN

(a) (b)

Set 1a

Set 1b

Bedding

Set 2a

Set 2b

Set 3a

Set 3b

51

3.7 General Considerations in Modelling Methodology

One of the main objectives of this thesis is to improve our general understanding

of the block caving induced subsidence phenomenon. It should be noted that the

ELFEN code is capable of modelling fracturing in both 2D and 3D space.

Although eventually full 3D mine scale analysis of block caving subsidence is

undoubtedly desirable, available modelling tools have yet to reach the

computational efficiency to allow a detailed and realistic 3D analysis. It is

suggested that parametric 2D analyses are an essential prerequisite to complex

three dimensional models if we are to further understand the factors controlling

caving and induced subsidence. In the current 2D modeling study emphasis is

given to the representation of the maximum level of detail possible with the

currently available computing power. The future development of 64 bit parallel

FEM/DEM with fracture codes will without doubt allow improved modelling in both

two and three dimensions. It is intended that the work presented in this thesis

will both demonstrate the immense potential of the FEM/DEM plus fracture

approach and provide a foundation for future more computationally intensive

research. Notwithstanding it should be stated that the models presented as part

of this thesis were in general run on high end PC‟s with the maximum available

RAM to 32 bit computers and involved runtimes of up to 25 days.

3.8 Summary

This chapter outlined the fundamental principles and advantages of the hybrid

FEM/DEM fracture mechanics based approach and its implementation in the

numerical code ELFEN. Clearly, application of this approach in combination with

DFN based fracture systems provides the opportunity to undertake physically

realistic modelling of a highly complex process such as block caving induced

surface subsidence development.

52

CHAPTER 4: USE OF EQUIVALENT CONTINUUM ROCK MASS PROPERTIES IN THE DISCRETE FRACTURE NETWORK FEM/DEM MODELLING OF BLOCK CAVING INDUCED SUBSIDENCE

4.1 Introduction

One of the key aspects in the numerical modelling of rock engineering problems

is establishing representative rock mass material strength and deformability

characteristics. This chapter

discusses available approaches to the derivation of jointed rock mass

mechanical properties;

examines the properties output from rock mass classification systems;

analyzes rock mass representation options within FEM/DEM plus

fracture modelling; and

presents a novel approach to the derivation and calibration of rock mass

properties specifically tailored for block caving subsidence analysis using

integrated DFN-FEM/DEM modelling.

4.2 Rock Mass Equivalent Continuum Mechanical Properties

On a scale of typical rock engineering analysis, such as the design of a civil/mine

opening or slope stability assessment, the rock mass material represents a

system comprised of intact rock regions separated by natural, pre-existing

discontinuities. The mechanical response of a jointed rock mass system is highly

complex and the material properties of the rock mass differ quantitatively by a

substantial but often unknown amount from laboratory tested intact rock

specimens. Usually in modern rock mechanics the rock mass is treated as an

equivalent continuum with scaled down strength and deformability characteristics

in order to account for the presence of discontinuities. The main equivalent

53

continuum rock mass mechanical properties required by most engineering

models include rock mass deformability and strength. Their description is given

below.

Rock mass deformability represents the combined deformability of the intact rock

material and the deformability of the discontinuity interfaces. The deformability of

the intact rock component is governed by its Young‟s modulus and Poisson‟s

ratio, whereas the normal and shear stiffness of a discontinuity interface governs

its deformation characteristics. The higher the density of the discontinuities,

generally, the more deformable the rock mass.

Rock mass strength parameters include uniaxial compressive strength, cohesion

and frictional strength, and uniaxial tensile strength. For the current ELFEN

analysis, uniaxial compressive strength is not used as a direct input parameter.

The rock mass cohesion is governed by the strength of the intact rock bridges

and the cohesive strength along the discontinuities interfaces. Fewer and less

persistent joints would result in higher cohesive strength of the rock mass. Good

joint surface contacts also contribute to higher cohesion. Similarly, the rock

mass friction angle is governed by two contributing components, the intact rock

internal friction angle and the friction along the discontinuity surfaces. In most

cases it is the frictional strength available of the joint surface which is the critical

factor. Rock mass friction generally depends on the orientation and persistence

of discontinuities, joint surface conditions (especially roughness) and presence of

infill.

Lastly, the intact rock can have a substantial tensile strength. On the rock mass

scale, typically, only a small component of the intact tensile strength can be

considered. Generally the tensile strength of the rock mass would depend on

persistence and density of discontinuities as well as amount of rock bridges and

quality of the jointing infill. The range in rock mass tensile strength could be from

nearly zero for heavily fractured rock masses up to nearly the intact rock tensile

strength for massive rock masses with very few discontinuities.

54

4.3 Derivation of Rock Mass Mechanical Properties

According to Jing (1998) the continuum approach trades material complexity for

geometrical simplicity, requiring proper homogenization techniques to identify the

material parameters associated with specified constitutive equations for the

equivalent continuum; the homogenization process is usually very complex and

valid only over a certain representative elementary volume. Cai et al. (2004)

indicated that there are so many parameters that affect the deformability and

strength of an arbitrary rock mass, it is generally impossible to develop a

universal law that can be used in any practical way to predict the mechanical

behaviour of the rock mass. As noted by Brady & Brown (2004) the

determination of the global mechanical properties of a large mass of

discontinuous in-situ rock remains one of the most difficult problems in the field of

rock mechanics. Clearly, establishing representative rock mass properties for

numerical modelling input is not a trivial task. Despite the apparent difficulty,

addressing this issue is unavoidable in any practical rock engineering analysis.

The principal approaches for determination of the basic mechanical characteristics

of a jointed rock mass include:

analytical solutions;

large scale in-situ testing;

numerically simulated large scale testing; and

empirical relationships based on rock mass classification systems.

4.3.1 Analytical Methods

Several closed form analytical solutions exist for description of the behaviour of a

jointed rock mass, among them Jaeger‟s (1960) and Wei‟s (1988) theories which

address the mechanical response of an axially loaded rock sample containing

several variously oriented discontinuities. Jaeger‟s plane of weakness theory

can be applied in several parts to determine the strength of the jointed rock

sample. Wei‟s theory gives a complete solution for derivation of the jointed rock

sample deformability, allowing incorporation of the effect of varying persistence.

55

It should be noted that these solutions have to date found limited practical

application as the required input data is seldom readily available.

4.3.2 In-situ Testing

It is possible to determine the rock mass strength and deformability characteristics of

a rock mass through “large scale” tests carried out in-situ. Traditional methods to

determine these parameters include compression tests for deformation modulus

(e.g. ASTM D4395 - 04) and block shear tests (e.g. Szymakowski, 2007) for shear

strength parameters. Generally the use of in-situ testing is complicated by the

difficulty in selecting and accessing the representative rock mass segment. These

methods are associated with high costs and therefore are applied only in rare cases.

4.3.3 Numerical Modelling

In recent years, numerical modelling methods are being increasingly employed for

deriving rock mass properties through simulated rock mass tests. The Particle

Flow Code, PFC, (Itasca, 2007), based on a “Synthetic Rock Mass” approach

(Pierce et al., 2007; Mas Ivars et al., 2007; Cundall, 2008) is a particularly

interesting development. It involves construction of a synthetic “sample” of the

rock mass in two or three dimensions by bonding together thousands of circular or

spherical particles. DFN based pre-inserted joints are introduced by debonding

particles along specific joint surfaces and employing a sliding joint model within the

PFC code. This approach overcomes the limitations of other numerical modelling

approaches to rock mass simulation in which the results are governed by a user-

specified constitutive model. Through strain-path driven loading of the “Synthetic

Rock Mass” samples the estimates of rock mass strength and brittleness can be

derived and used as a direct input to standard continuum models. Reyes-Montes

et al. (2007) performed a validation study of the Synthetic Rock Mass approach

and found a good correlation between the fracturing orientation and modes

predicted by the PFC models and those observed from in-situ recorded

microseismicity at Northparkes block cave mine. Overall, it should be emphasized

56

that this approach is still being refined and further work is ongoing to illustrate its

applicability in the analysis of a range of practical rock engineering problems.

4.3.4 Empirically Based Rock Mass Classification Systems.

Empirical rock mass classification systems are perhaps the most widely used tool

for the assessment of rock mass engineering behaviour. According to Brady &

Brown (2004), classification systems seek to assign numerical values to those

properties or features of the rock mass considered likely to influence its behaviour,

and to combine these individual values into one overall classification rating for the

rock mass. There are more than 20 different rock mass classification systems (see

review by Edelbro et al., 2006). The most commonly used are the Rock Mass

Rating RMR76 (Bieniawski, 1976), the Tunnelling Quality Index Q (Barton et al.,

1974) and the Geological Strength Index GSI (Hoek, 1994). Table 4.1 lists

parameters utilized in the rating calculation for these systems.

Table 4.1 Rock mass parameters used in rock mass rating by RMR76, Q and GSI

RMC system Classification parameters Rating values

RMR76 UCS, RQD, Joint spacing, Joint conditions, Ground water conditions, (adjustments for joint orientation)

8 … 100

Q Joint set number (Jn), RQD, Joint roughness (Jr), Joint alteration (Ja), Joint water reduction factor (Jw), Stress reduction factor (SRF)

0.001 … 1000

GSI Rock mass blockiness, joint surface conditions 5 … 100

The RMR and Q systems were initially developed to provide assessment of rock

mass quality for tunnelling, their application later expanded to a wider field of rock

engineering problems. Accumulated experience of applying these rating systems

has led to the development of empirical correlations between rock mass rating and

basic mechanical properties. The GSI rock mass classification system was

developed specifically to provide input data for engineering analysis. It relies on

fewer parameters and is built around the Hoek-Brown failure criterion (Hoek et

al., 2002). Empirical correlations exist between the GSI rating, rock mass

deformability and Hoek-Brown failure criterion parameters. A summary of RMR,

57

Q and GSI based empirical relationships for estimation of mechanical properties

of the rock mass is given in Table 4.2. To appreciate the applicability and

limitations of these relationships it is important to understand their origin.

Table 4.2 Empirical relationships for derivation of estimates of basic rock mass strength and deformability properties based on the RMR, GSI and Q rock mass classification systems

RMC System

Estimates of Rock Mass Strength and Deformability Characteristics

Reference

RMR

40/)10(10 RMRmE (GPa)

2/5 RMR

RMRc 5 (kPa)

Serafim & Pereira (1983)

Bieniawski (1989)

Q

31

10 cm QE (GPa)

1tan"" 1 w

a

r J

J

J

100

1"" c

n SRFJ

RQDc (MPa)

where:

)100/( cc QQ - normalized Q;

c – uniaxial compressive strength (MPa)

Barton (2002)

GSI

)11/)1560((1

2/102.0

GSIDime

DEE (MPa)

1'3

1'3'

6212

6sin

a

nbb

a

nbb

msamaa

msama

aamsamaa

msmasac

a

nbb

a

nbnbci

216121

121

1'3

1'3

'3' (MPa)

where:

Ei – intact rock Young‟s modulus;

D - disturbance factor;

a, s, mb – material constant;

cn /'max33 , '

max3 - upper limit of confining stress

Hoek et al. (2002)

Hoek & Diederichs

(2006)

The RMR and Q correlations for the Young‟s modulus originated from the dataset

of in-situ tests compiled by Bieniawski (1978) and Serafim & Pereira (1983), both

58

correlations were derived through exponential fit to the data, Fig. 4.1. Recent

GSI correlations are founded on a different dataset compiled from in-situ testing

data from China and Taiwan. The Hoek & Diederichs (2006) GSI correlation of

rock mass Young‟s modulus to GSI rating is based on a sigmoidal fit to the

experimental data in order to constrain the increase of the modulus as the rock

becomes more massive, Fig. 4.2.

Fig. 4.1 RMR, Q and rock mass deformation modulus correlations

Fig. 4.2 GSI and rock mass deformation modulus correlation proposed by Hoek & Diederichs (2006)

Bieniawski (1979) suggested approximate ranges of cohesion and friction angles

for particular RMR ranges. In a later version of the RMR classification system

59

(Bieniawski, 1989), used these ranges to propose simple relationships correlating

RMR, rock mass cohesion and friction.

The GSI does not provide a direct estimate of rock mass cohesion and friction, as

there is no direct correlation between the linear Mohr-Coulomb criterion and the

non-linear Hoek-Brown criterion. The estimates of these parameters are

computed through a procedure that involves simulating a set of triaxial strength

tests using Hoek-Brown criterion then fitting the Mohr-Coulomb linear failure

envelope to the resulting Mohr‟s circles through linear interpolation, thus allowing

computation of c and υ. Care should be exercised when selecting the „best‟ linear

line in fitting the Mohr circles. Generally it depends on the level of confining stress

for a particular engineering application. For a slope problem, the confining stress

may vary from zero to some level of stress (usually related to the height of the

slope). Curvature of the non-linear Hoek-Brown strength envelope is greatest at

low confinement stresses, and for this region the fitting procedure is particularly

sensitive to the assumed stress. For a tunnel problem, if the depth and stress

range are known, the linear envelope should be fitted best for the Mohr circles in

the stress region of interest (Hoek & Brown, 1997; Hoek et al., 2002).

Barton (2002) gives a detailed rationale for the proposed Q correlations for

estimation of jointed rock mass cohesion and friction. Jointed rock mass cohesion

in Q correlation is derived from the “massiveness” of the rock mass, expressed

through the RQD/Jn ratio. Massive, highly stressed rock masses with high

cohesive strength suffer the greatest reduction in block-size and cohesive strength,

as a result of stress-induced fracturing around deep excavations, therefore it is

important to adjust the cohesion estimates for the effect of stress. Generalization

of the cohesion estimate is achieved through normalization with c/100. The

jointed rock mass friction in the Q correlation is governed by the conditions at the

discontinuity contacts. Barton (2002) argued that the Jr/Ja ratio closely resembles

the dilatant or contractile coefficient of friction for joints and filled discontinuities.

Back-calculation of case records showed that tan-1(Jr/Ja) provided realistic

estimates of the friction angle on the discontinuity surfaces. To account for the

60

potential effect of ground water the Jw reduction factor was included in the

correlation. It was noted that the Jr and Ja ratings should be derived for the

discontinuities most affecting the result of the particular loading direction.

There is an extensive discussion in the literature about the use and misuse of rock

mass classification systems (see Milne et al., 1998; Stille & Palmstrom, 2002;

Marinos et al., 2005). The validity of mechanical properties derived using different

systems is also a subject of considerable debate. Marinos et al. (2005) argued

that the ground water and structural orientation parameters in RMR and the

groundwater and stress parameters in Q are dealt with explicitly in effective stress

numerical analyses and the incorporation of these parameters into the rock mass

property estimate results is inappropriate. Barton (2007) asserted that: “GSI-

based Hoek-Brown formulations for “simple” geotechnical input data for the rock

mass, such as deformation modulus, cohesion and friction angle, appear to have

reached „black-box‟ levels of complexity, which seems to be detrimental to the idea

of rock engineering, if engineering judgement is still to be exercised in this

rewarding field of engineering”.

Notwithstanding the uncertainties and limitations, rock mass classification systems

remain a primary source for estimation of equivalent continuum rock mass strength

and deformability characteristics in practical rock engineering analyses. The

following section compares the properties derived from rock mass properties

correlations given in Table 4.2.

4.4 Comparative Study of Rock Mass Strength and Deformability Parameters Derived through RMR76, GSI and Q Rock Mass Classification Systems

4.4.1 Properties Derivation

It is a common practice in rock engineering to use the rating from one

classification system to estimate the value of another. A number of cross-

correlations between RMR, GSI and Q systems ratings were suggested over the

years (see review by Milne et al., 1998; Ramamurthy, 2004). According to Milne

61

et al. (1998), the equation proposed by Bieniawski (1976), linking RMR76 and Q,

is the most popular correlation:

44ln976 QRMR (4.1)

Hoek et al. (1995) suggested that for dry RMR76 > 18:

76RMRGSI (4.2)

Given the intrinsic interrelationship between the RMR, GSI and Q ratings, it is

possible to compare the rock mass properties estimated by these classification

systems for the same rating value. Based on this proposition, a fictitious dry, hard

rock mass with fair joint surface conditions was considered. For this rock mass,

based on the RMR, GSI and Q systems, four cases with varying rock mass quality

ratings equivalent to RMR76 80, 70, 60 and 50 were derived and corresponding

rock mass properties were estimated, as shown in Tables 4.3 to 4.5. Here it should

be noted that extreme care was taken to maintain consistency in the rock mass

conditions between the fictitious cases across studied classifications systems. The

comparison discussed here is based on an assumption that comparative RMR76, Q

and GSI ratings should yield similar mechanical properties.

Table 4.3 Rock mass properties derived using RMR76

Rating Criteria

RMR76 Rock Mass

RMR 80 RMR 70 RMR 60 RMR 50

UCS, MPa 100 - 250 (12)* 100 - 250 (12) 50 - 100 (7) 50 - 100 (7)

RQD 75%-90% (17) 50%-75% (13) 25%-50% (8) <25% (3)

Spacing of discont.

0.6 – 2m (15) 0.2 -0.6m (10) 0.2 -0.6m (10) <0.06m (5)

Joint conditions

Length 1-3m (4) Separ. 0.1-1mm (4) Smooth (1) No infill (6) Unweath. (6)




Water cond Dry (15) Dry (15) Dry (15) Dry (15)

Estimated rock mass properties

E=56GPa c=0.4MPa

=45 σt =0.33MPa**

E=32GPa c=0.35MPa

=40 σt =0.33MPa

E=18GPa c=0.3MPa

=35 σt =0.31MPa

E=10GPa c=0.25MPa

=30 σt =0.29MPa

* - RMR rating value; ** - derived using Mohr-Coulomb criterion: sin1

cos2ct

62

Table 4.4 Rock mass properties derived using Q

Rating Criteria

Q Rock Mass

Q 47.5 (RMR79)

Q 17.5 (RMR 70)

Q 6.2 (RMR 60)

Q 0.67 (RMR 50)

Block size RQD=95% 1 joint set, Jn=2

RQD=70% 2 joint sets, Jn=4

RQD=37% 2 joint sets + random, Jn =6

RQD=12% 3 joint sets, Jn=9

Inter block shear strength

Smooth, planar joints, Jr =1; Unaltered joint walls, Ja =1




Active Stress

Dry: Jw=1; Medium stress: SRF=1





for σc =110MPa E=37GPa c=52MPa

=45 σt=43MPa* (no cut off) σt=22MPa (50% cut off) σt=4.3MPa (90% cut off)

for σc=100MPa E=26GPa c=15MPa

=45 σt=13MPa (no cut off) σt =6.3MPa (50% cut off) σt =1.3MPa (90% cut off)

for σc=90MPa E=18GPa c=4.7MPa

=45 σt=3.9MPa (no cut off) σt =1.8MPa (50% cut off) σt =0.4MPa (90% cut off)

for σc=80MPa E=12GPa c=1.6MPa

=45 σt=1.3MPa (no cut off) σt =0. 7MPa (50% cut off) σt =0.1MPa (90% cut off)

* - derived using Mohr-Coulomb criterion

Table 4.5 Rock mass properties derived using GSI

Rating Criteria

GSI Rock Mass

GSI 80 (RMR 80)

GSI 70 (RMR 70)

GSI 60 (RMR 60)

GSI 50 (RMR 50)

UCS, MPa 110 100 90 80

mi 15 15 15 15

γ, MN/m3 0.026 0.026 0.026 0.026

Ei, GPa 60 60 60 60

D 0 0 0 0


E=53GPa c=4.9MPa

=57 σt =1.6MPa*

E=44GPa c=2.9MPa

=57 σt =0.8MPa

E=31GPa c=2 MPa

=55 σt =0.4MPa

E=18GPa c=1.4MPa

=53 σt =0.2MPa

* - derived using Mohr-Coulomb criterion

The strength and deformability property estimates for the RMR and Q systems

were computed directly based on the equations given in Table 4.2, and the GSI

derived properties were established using the RocLab v1.031 program

(Rocscience Inc., 2007), which is based on the GSI equations given in Table 4.2.

63

It should be noted that the GSI allows property estimates to be tailored to slope

stability analyses, as well as for tunnelling. The current study deals with

underground mining simulation and therefore assumed a tunnel located at 200m

(i.e. corresponding to a moderate stress level in the Q system correlation).

Fig. 4.3 compares the estimates of rock mass Young‟s modulus, friction angle,

cohesion and tensile strength derived using RMR76, Q and GSI systems, expressed

through equivalent RMR76 rating. Fig. 4.4 shows the relative change in the

magnitude of the above mentioned parameters with increasing rock mass rating.

(a) Deformation modulus

10

32

56

18

31

44

53

11 18

26 37

0

10

20

30

40

50

60

50 60 70 80

Defo

rmati

on

mo

du

lus, G

Pa

RMR

RMR

GSI - tunnel (-200m)

Q

(b) Friction angle

30

35

40

45

5355 57

57

4545 45

45

0

10

20

30

40

50

60

50 60 70 80

Fri

cti

on

an

gle

, d

eg

rees

RMR

RMR


Q

(c) Cohesion

0.25

0.3 0.35 0.41.4

22.9

4.9

1.6

4.7

15

0

2

4

6

8

10

12

14

16

18

20

50 60 70 80

Co

hesio

n, M

Pa

RMR

RMR


Q

52 / 80

(d) Tensile Strength

0.31 0.330.330.2

0.8 1.61.3

4

13

0.7

1.8

6.3

0.1

0.41.3

4.3

0

5

10

15

50 60 70 80

Ten

sile s

tren

gth

, MP

a

RMR

RMR


Q

Q - 50% cut-of f

Q - 90% cut-of f

43 / 80 22 / 80

Fig. 4.3 Comparison of rock mass strength and deformability characteristics derived using RMR76, Q and GSI RMC systems (a) deformation modulus; (b) friction angle; (c) cohesion; (d) tensile strength

64

(a) RMR

78

216

462

20 40 6017 33 50

8 13 150

200

400

600

800

1000

60 70 80

Mag

nit

ud

e in

cre

ase in

%o

f R

MR

50 v

alu

e

RMR

Deform. modulus

Cohesion

Friction

Tensile Strength

(b) GSI

70

139187

43107

250

4.4 7.4 8.2

112

371

841

0

200

400

600

800

1000

60 70 80

Mag

n. i

ncre

ase in

%o

f eq

uiv

. R

MR

50 v

alu

e

Equivalent RMR

Deform. modulus

Cohesion

Friction

Tensile Strength

(c) Q

59

133

234194

843

3150

0 0 0

200

861

3238

0

200

400

600

800

1000

60 70 80

Mag

n. i

ncre

ase in

% o

f eq

uiv

. R

MR

50 v

alu

e

Equivalent RMR

Deform. modulus

Cohesion

Friction

Tensile Strength

Fig. 4.4 Percentile change in properties magnitudes with increasing rock mass rating (a) RMR based properties; (b) GSI based properties; (c) Q based properties

4.4.2 Rock Mass Deformation Modulus

According to Fig. 4.3(a), the estimates of rock mass deformation modulus

derived using the three different rock mass classification systems exhibit

generally similar trends. The GSI correlation yields deformation modulus values

in a range of 18 to 53 GPa which are consistently higher than those by other

systems, with the exception of an equivalent RMR of 80 where the RMR

predicted modulus is about 3 GPa higher. The Q correlation yields values which

are about 30-40% lower than those predicted by GSI (12 - 37 GPa). The RMR

65

correlation curve follows the Q curve for RMR 50 to 60 and then steeply rises.

Fig. 4.4 indicates that with the increase of rock mass rating from RMR 50 to RMR

80, the RMR based deformation modulus estimate increases by more than five

times (from 10 to 56 GPa), whereas GSI and Q based estimates only doubled. It

is rather difficult to make a definitive judgement on which system yields more

appropriate modulus values, as all systems are based on interpretation of actual

measured data. The recently proposed GSI correlation is based on a large

number of case histories and has been rigorously verified, as reported by the

authors. However, GSI estimates appear to be less conservative. More practical

applications are needed to gain confidence in GSI based modulus correlation.

Overall, the Q correlation appears to yield adequately conservative values, with

respect to deformation modulus, throughout the studied rating range.

4.4.3 Rock Mass Friction Angle

As follows from Fig. 4.3(b) the estimates of rock mass friction angle derived using

RMR and GSI exhibit an increase in rock mass friction angle with increase in

rock mass rating. Friction angle estimates in the Q correlation are solely

dependant on joint surface conditions. For the purpose of the current analysis,

identical joint surface conditions were assumed, with Q correlations yielding a

constant friction angle of 45 degrees. It should be noted that sole dependence of

friction estimates on joint surface conditions in some cases may lead to very low

estimates of friction angle. As reported by Barton (2002), estimates of the friction

angle of discontinuity interfaces with clay infill can be as low as a few degrees. It

appears unreasonable to assume that an equivalent continuum rock mass would

have such a low friction angle. If the discontinuities with very low frictional

characteristics are present they must be incorporated into the equivalent

continuum analysis explicitly, or alternatively, a discontinuum analysis should be

considered. GSI correlations yielded high friction angle estimates of more than

50 degrees, although only a slight change in the magnitude (less than 10%) was

observed with increasing rock mass rating. Justifying such high friction angle

values is rather difficult, particularly for the rock mass with lower rating. RMR

66

based friction angle estimates vary by 15 degrees over the studied rating range,

from 30 degrees for RMR 50 to 45 degrees for RMR 80. It appears that RMR

correlation produces overall realistic estimates of the rock mass friction angle.

4.4.4 Rock Mass Cohesion

Fig. 4.3(c) shows the variation of the rock mass cohesion estimates for different

equivalent RMR ratings. As shown in this figure and Fig. 4.4, cohesion estimates

differ quite dramatically between the RMR, GSI and Q systems. RMR based

correlation produces a very narrow range of very low rock mass cohesion

estimates, less than 0.4 MPa, which is comparable to the cohesive strength of

stiff clays. Barton (2002) noted that such estimates give the impression of far too

low a cohesion for hard rock, and was perhaps estimated from experience of coal

measure rocks, from which many RMR case records were derived. Overall, it

appears that RMR based cohesion estimates are overly conservative. The GSI

based correlation produces more reasonable values, roughly an order of

magnitude higher than RMR. The Q correlation shows an exponential trend,

giving a very broad cohesion range, so that an equivalent RMR 80 cohesion

estimate of 52 MPa is more than 30 times higher than its equivalent RMR 50

counterpart and more than 100 times higher than the RMR based cohesion for

the same rating. It appears that the Q correlation tends to overestimate rock

mass cohesion for higher ratings (equivalent RMR>60), where cohesion

estimates approach high values characteristic of very strong intact rock.

4.4.5 Rock Mass Tensile Strength

Rock mass tensile strength estimates for RMR, GSI and Q systems are shown in

Fig. 4.4(d). It should be noted that only the GSI allows direct estimates of rock

mass tensile strength. GSI estimated values are in the range 0.2 to 1.6 MPa, for

a corresponding equivalent RMR of 50 to 80. The estimates of tensile strength

below 0.3 MPa for RMR<60 seems to be very low, GSI estimates for the

remaining range seems to be reasonably realistic. For RMR and Q, the tensile

strength was derived using cohesion and friction values and the Mohr-Coulomb

67

relationship (see Table 4.3). It is well recognized that the Mohr-Coulomb based

tensile strength over predicts the actual values and an adjustment through a

“tensile cut-off” is necessary. As discussed in Section 4.2.1, the rock mass

tensile strength may vary over a wide range depending on the density of

discontinuities and deriving a representative tensile cut-off in such circumstances

can be challenging. Provided that the RMR estimated cohesion is within the kPa

range, for the studied rating values the derived tensile strength is about 300 kPa.

Application of a tensile cut-off to such low values is not particularly meaningful.

In contrast, high values of cohesion for Q result in very high tensile strength

estimates, up to 60 times larger than for RMR. Here application of a tensile cut-

off is required. Two cut-off assumptions were considered, 50% and 90%. It

appears that the assumption of a 90% cut-off yields generally realistic tensile

strength estimates for an equivalent RMR>60.

4.4.6 Summary

In summary, comparison of strength and deformability properties derived from

the RMR, Q and GSI systems for corresponding rating values for the most part

showed a lack of consistency. The following can be concluded from this

comparative study:

RMR based correlations produce generally reasonable estimates of rock

mass deformation modulus and friction angle, but yield extremely low

values of cohesion and consequently very low tensile strength estimates.

GSI based correlations produce generally realistic estimates of rock mass

mechanical properties although the friction angles indicated are higher in

comparison to RMR and Q. Deformation modulus estimates produced by

the GSI correlation appear to be stiffer and less conservative than other

methods.

Q based deformation modulus correlation yields reasonably conservative

estimates. Estimates of rock mass cohesion appear to be very high for

higher Q ratings. Friction angle estimates are solely dependant on

conditions along the discontinuities interfaces, which may result in very

68

conservative values. Using the derived cohesion values the calculated

rock mass tensile strength requires the assumption of a substantial tensile

cut-off to achieve reasonable tensile strength estimates.

4.5 Evaluation of Applicability of Rock Mass Classifications Derived Equivalent Continuum Properties for Modelling of Block Caving Induced Surface Subsidence

Analyses presented here evaluate the use of rock mass classification systems as

a source of equivalent continuum properties for integrated FEM/DEM-DFN

modelling of block caving induced surface subsidence. A series of numerical

experiments were carried out to investigate the behaviour of a system comprised

of key discontinuities and an equivalent continuum rock mass derived using

varying assumptions for mechanical properties from rock mass classification

systems.

4.5.1 Modelling Methodology

4.5.1.1 Model Setup

A 4000m x 600m ELFEN model sub-divided into non-fracturing and fracturing

regions was used, see Fig. 4.5. The fracturing region spans up to 1000m and

covers the principal area where fractures may potentially develop and has a

higher mesh resolution (2m sized elements). The non-fracturing region has a

lower discretization density (up to 50m elements) and is required to extend to the

model boundaries to minimize potential boundary effects on simulation results. A

sensitivity analysis of the assumed boundary conditions, illustrated that the

adopted model size and boundaries for the fracturing and non-fracturing regions

are adequate for the current modelling, i.e. the effect of the boundary conditions

on modelling domain is negligible. Flores & Karzulovic (2002) studied a number

of block caving mines and reported typical caved ore block heights of around

200m. In the current study, block caving mining is simulated by undercutting and

full extraction of a block of ore (100m x 100m) located within the fracturing region

at 200m depth. The undercut (100m x 4 m) is developed in stages in 20m

69

increments. A uniform draw of ore is assumed. With respect to simulation of the

ore extraction there are generally two options:

Option 1. Looped (repeated) deletion of the caved material (discrete

elements) within the full length of the undercut level;

Option 2. Uniform material withdrawal by gradual lowering of the undercut

floor, as illustrated in Fig. 4.5.

70

Caveability Laubscher’s caveability chart

Cave development

progression

Conceptual model of caving

by Duplancic & Brady (1999)

Subsidence limits Mining experience

Caveability Laubscher’s caveability chart

Cave development

progression

Conceptual model of caving

by Duplancic & Brady (1999)

Subsidence limits Mining experience

Model geometry

Non-fracturing zone

Fracturing zone

100m

ore

block

100m

100m

70o

20o4m

FracMan 3D model 2D trace planefractures

exported

into ELFEN

Constraints

model response

evaluation

4000m

600m

Model setup

140m

undercut

moving platform

Fig. 4.5 ELFEN model setup and response evaluation procedure

71

Initial modelling trials showed that use of the first option is complicated by the

fact that simultaneous deletion of the caved fragments in the 4m high undercut

triggered sudden collapse of the overlying rock mass, causing shock loading of

the system and creating numerical noise which complicated interpretation of

surface displacements. Significantly smaller looped deletion region heights could

not be considered as available code functionality only allows deletion of discrete

elements fully enclosed in a specified rectangular region and the minimum

element size assumed for the current modelling was 2m. For the above reason

option two was adopted for the current modelling. Similar methodology was

utilized for physical model test studies of caving by Kvapil (2004) as illustrated in

Fig. 4.6. Isotropic material properties were assumed throughout the model and

the draw was continued until the volume of rock equivalent to the volume of the

ore block is extracted.

Fig. 4.6 Physical model of progressive caving development (adapted after Kvapil, 2004 with permission).

72

Mahtab et al. (1973) noted that the fracture system most favourable for caving

includes a low dipping and two nearly orthogonal steeply dipping joint sets. The

3D FracMan DFN model adopted in the current analysis incorporated one

horizontal and two orthogonal vertical sets with widely spaced and moderately

persistent joints. The joint pattern for the 2D model was derived by assuming a

plane parallel to one of the vertical sets within the 3D DFN model. Joint traces

intersecting this plane were delineated and exported into ELFEN. Imported joint

sets were rotated with respect to the model centre to achieve the desired dip.

The following joint orientations were adopted: one sub-vertical set dipping at 70°

and one orthogonal sub-horizontal set (Fig. 4.5). It should be emphasized that

for the current study all modelling was based on a single FracMan realization.

Generated joints were assumed to represent key discontinuities governing rock

mass response.

Representation of the rock mass strength and deformability in the inter-joint

regions was based on the properties derived from the RMR and Q correlations.

GSI correlations were not used in the current analysis. Hoek et al. (2002) stated

that for studies of problems such as block caving in mines it is recommended that

no attempt should be made to relate the Hoek-Brown and Mohr-Coulomb

parameters. Correlations relating these parameters are valid only for cases

where the zone of failure does not extend to the surface.

Estimates of the RMR and Q system based rock mass properties derived in

Section 4.2.3 were utilized. It was assumed that pre-inserted discontinuities

have no cohesive strength and have a friction angle of 35 degrees. As discussed

in Section 3.5.4 the normal penalty at the pre-inserted fractures interface can

effectively be considered equivalent in magnitude to the joint normal stiffness.

Similarly, the tangential penalty was taken as equivalent to the joint shear

stiffness. An estimate of the joint tangential penalty was derived using a

correlation proposed by Barton (1982), see Fig. 4.7. A corresponding normal

penalty was taken as equal to 10Pt, as recommended in the ELFEN manual

(Rockfield, 2007).

73

0.2

Fig. 4.7 Derivation of joints shear stiffness using Barton‟s (1982) correlation

4.5.1.2 Modelling Scenarios

Modelling scenarios and corresponding input parameters are summarized in

Table 4.6. Modelling was carried out in two stages. The first stage focused on

evaluation of the simulated caving response. For each modelling scenario

undercutting of 20x20m, 40x40m and 60x60m blocks and their full or partial

extraction was considered. At the second stage, cave progression and

subsidence development were analyzed, considering a 100x100m block.

Flores & Karzulovic (2002) summarized in-situ stress measurement data from a

number of block caving mines and reported median Kmean of 1.2 with standard

deviation of 0.5. For the current modelling, initial stress conditions assumed

vertical/horizontal orientation of principal stresses, a default value of in-situ stress

ratio K of 1 was adopted.

Secant shear stiffness

(GPa/m)

Approx. normal stress (MPa)

structures in models

structures with clay gouge

structures in rock

active geological faults

Ks = τ / δ

10mm 1m 100m 10km 1000km Length of the Structure (subjected to shear)

100

10

1

0.1

0.01

0.001

0.0001

74

Table 4.6 List of principal modelling scenarios and corresponding input parameters

Mo

de

llin

g s

ce

na

rio

s

Input parameters

Rock Mass Discontinuities

De

form

atio

n m

odu

lus,

E, G

Pa

Co

he

sio

n,

ci,

MP

a

Friction

, I d

eg

ree

s

Ten

sile

str

ength

, t,

MP

a

Po

isso

n‟s

ra

tio

* ,

De

nsity

* , ρ

kgm

-3

Dila

tion

* , ψ

deg

ree

s

Fra

ctu

re e

nerg

y* ,

Gf

Jm

-2

Inte

rfa

ce c

ohe

sio

n* ,

cf, M

Pa

Inte

rfa

ce frictio

n* ,

f ,

deg

ree

s

No

rma

l p

en

alty,

Pn, G

Pa

/m

Tan

ge

ntia

l p

en

alty,

Pt,

GP

a/m

RMR80 56 0.4 45 0.33

0.25 2600 5 60 0 35 2 0.2

RMR70 32 0.35 40 0.33

RMR60 18 0.3 35 0.31

RMR50 10 0.25 30 0.29

Q 47.5 (equiv. to RMR 79)

37 52 45 13

(70% c.o.**)

37 52 45 4.3

(90% c.o.)


26 15.1 45 4.3

(70% c.o.)

26 15.1 45 1.25

(90% c.o.)


18 4.7 45 1.18

(70% c.o.)

18 4.7 45 0.46

(90% c.o.)


12 1.6 45 0.4

(70% c.o.)

12 1.6 45 0.13

(90% c.o.)

* assumed based on estimates for Carbonatite ore at Palabora mine (Rockfield, 2003) ** assuming maximum tensile strength at zero cut off

4.5.2 Constraining Criteria

In order to evaluate if behaviour simulated using the varied strength and

deformability properties sets is realistic, it should be constrained against

observed response. The constraining criteria adopted for the current analysis

are given in Fig. 4.8.

75

The first stage of block caving is undercutting the ore block. The ore must be

undercut beyond a certain hydraulic radius (area/perimeter) to provide continuous

caving. Laubscher‟s caveability chart (Diering & Laubscher, 1987) is perhaps the

most widely accepted measure of rock mass caving susceptibility. Based on a

number of cave mining case studies Laubscher delineated zones of varying rock

mass response to caving depending on rock mass rating and dimensions of the

undercut, as shown in Fig. 4.8(a). This criterion was employed as one of the three

approximate constraints for evaluating how realistic the simulation of rock mass

caveability is.

Block undercutting is followed by continuous ore extraction, which triggers

propagation of the caving front upwards. To date, cave propagation behaviour is

far from being fully understood. The available descriptions of caving

mechanisms are qualitative and largely based on tentative interpretations of the

microseismic data. A conceptual model of cave propagation by Duplancic &

Brady (1999), shown in Fig. 4.8(b), is the most widely cited. It was developed

based on the analysis of seismic monitoring data at early stages of caving at

Northparkes E26 block cave. The conceptual model consists of four main

regions: (1) pseudo-continuous domain, where the rock mass is mainly

undisturbed; (2) seismogenic zone, where seismic events occur due to slip on

joints and brittle failure of rock, caused by changing stress conditions related to

the advancing caving front; (3) zone of discontinuous deformation, where the

rock mass provides minimal support to the overlying strata and rock

disintegration occurs; and (4) caved zone and air gap, where the rock blocks that

have fallen from the cave come to rest, and where an air gap may form if there is

a difference between extraction and caving rates (Fig. 4.5b). The Duplancic &

Brady concept was adopted in this study as a second constraint for assessment

of simulated caving behaviour.

Continuous ore extraction eventually leads to the formation of a surface

subsidence zone. A cave mining experience-based rule of thumb (see Section

2.5.1) was utilized as the third subsidence constraining criterion. It was assumed

76

that major surface deformations should not exceed 45 degree limiting angles

drawn from the bottom of the undercut, as shown in Fig. 4.8(c).

Simulated behaviour that tentatively met all three constraining criteria was

deemed acceptable and corresponding equivalent continuum properties

adequately representative.

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80

Mo

dif

ied

Ro

ck M

ass R

ati

ng

(M

RM

R)

Hydraulic Radius, m

stable zonetransition

zone

caving zone

45o45o

Fig. 4.8 Constraints for ELFEN modelling of block caving induced subsidence

(a) Laubscher‟s caveability chart; (b) Conceptual model of cave propagation (Duplancic & Brady, 1999); (c) Subsidence limits

4.5.3 Modelling Results

Modelling results based on RMR and Q property sets are presented in Figs. 4.9

to 4.16. Figs. 4.9 to 4.11 illustrate simulated rock mass response to caving for

varying undercut dimensions. Fig. 4.12 summarizes simulated caveability

(c)

(a) (b)

77

response and compares it with Laubscher‟s empirical caveability chart. In this

figure rock mass caveability was evaluated based on the following assumptions:

stable conditions were assumed if the cave could not propagate up to the

block centre;

transitional conditions were assumed if the cave propagated more than a

half, but less than the full block height;

caving conditions were assumed if the cave front exceeds block height.

MRMR estimates were based on the assumption of MRMR 0.9RMR

(Flores & Karzulovic, 2002).

Figs. 4.13 to 4.15 show cave development progression at early stages of ore

extraction. Figs. 4.16 and 4.17 show simulated surface subsidence.

4.5.3.1 Simulations with RMR Properties

As illustrated in Figs. 4.9 and 4.12(a), simulations based on RMR properties

showed largely realistic response to caving, from high caveability at RMR=50 to

nearly stable conditions at RMR=80. Modelling results are in overall agreement

with Laubscher‟s caveability chart, although it appears that simulations based on

RMR properties tend to overestimate caveability of the rock mass. Simulated cave

development behaviour, shown in Fig. 4.13, differs quite significantly from the

Duplancic & Brady concept; an overly soft response is observed, the crown pillar

fractured very rapidly, and a clear distinction between the stable and seismogenic

zones cannot be made. The ellipsoid failure pattern formed during ore extraction

indicates mobilization of significant rock volumes even at early stages of ore

extraction, regardless of the rock mass rating. It should be noted that such failure

is characteristic of soft rock conditions. Further simulation of caving progression

up to subsidence development showed that RMR based properties tend to grossly

overestimate the amount of damage and extent of rock mass deformations caused

by caving (see Fig. 4.16), the only exception is RMR=80.

Overall, none of the considered RMR property sets produced simulated

behaviour agreeing with all three constraining criteria. Excessive fracturing

78

associated with the use of RMR properties can be attributed to the very low

estimates of rock mass tensile strength given by this system. Interestingly the

significant decrease in rock mass deformability, with increasing RMR rating,

restricted the rock mass caveability.

4.5.3.2 Simulations with Q Properties

Two Q based property sets were considered using tensile strength cut-off

assumptions of 90% and 70%.

As follows from Figs. 4.10 and 4.12(b) simulations based on 90% cut-off

assumption tend to underestimate caveability at smaller undercut dimensions

(Hr=20), but overall produce reasonable fits with the empirical data at larger

undercuts (Hr=30), exhibiting a realistic trend of decreasing caveability with

higher rating. According to Fig. 4.10, simulation of cave propagation based on

these properties set does not show a reasonable agreement with the Duplancic &

Brady concept, with the exception of the Q 17.5 case (equivalent RMR70). For

this property set gradual cave propagation was observed. Simulations with lower

Q properties produced rapid, rather sporadic caving. For higher Q values caving

could not be simulated due to apparent cave arrest. Subsidence simulation

based on Q properties with 90% cut-off is shown in Fig. 4.17. A Q of 0.67

(equivalent RMR=50) and a Q of 6.2 (equivalent RMR=60) resulted in excessive

fracturing and overestimated the extent of surface deformations. The Q=17.5

property set produced reasonable subsidence extent predictions.

Simulations based on a 70% cut-off assumption underestimated the caving

response for the studied undercut dimensions, see Figs. 4.11 and 4.12(c). In

terms of cave propagation a Q of 0.67 property set resulted in excessively rapid

caving. A Q of 6.2 showed reasonable cave propagation, and a Q of 17.5 and

47.5 could not be analysed due to limited caving. Subsidence modelling based

on a Q of 0.67 produced an unrealistically large zone of subsidence

deformations, whereas subsidence predictions based on a Q of 6.2 were

generally reasonable, Fig. 4.17.

79

Overall, only two selected Q property sets (Q=17.5 with 90% cut-off and Q=6.2

with 70% cut off) showed a reasonable agreement with all three constraining

criteria. Interestingly, for the Q property sets, an excessively soft response was

observed for lower Q ratings and an excessively stiff response was observed for

higher ratings. Middle range values produced apparently reasonable behaviour.

This can be explained by high variability of tensile strength estimates which varied

from 0.13 MPa (Q=0.67 90% cutoff) to 13 MPa (Q=47.5 70% cutoff). Simulations

exhibiting reasonable behaviour had a tensile strength of about 1.2 MPa.

80

Hr10 Hr20 Hr30

RMR 50

RMR 60

RMR 70

RMR 80

Fig. 4.9 Caving response with RMR equivalent continuum properties

81

Hr10 Hr20 Hr30

Q 0.67

90% c.o.

Q 6.2 90% c.o.

Q 17.5 90% c.o.

assumed stable

Q 47.5 90% c.o.

assumed stable assumed stable

Fig. 4.10 Caving response with Q equivalent continuum properties (90% tensile c.o.)

82

Hr10 Hr20 Hr30

Q 0.67

70% c.o.

Q 6.2 70% c.o.

Q 17.5 70% c.o.

assumed stable

Q 47.5 70% c.o

assumed stable assumed stable assumed stable

Fig. 4.11 Caving response with Q equivalent continuum properties (70% tensile c.o.)

83

(a)

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80

Mo

dif

ied

Ro

ck M

ass R

ati

ng

(M

RM

R)

Hydraulic Radius, m


zone

caving zone

Legend:

stable

transitional

caving

(b) (c)

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80

Mo

dif

ied

Ro

ck M

ass R

ati

ng

(M

RM

R)

Hydraulic Radius, m


zone

caving zone

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80

Mo

dif

ied

Ro

ck M

ass R

ati

ng

(M

RM

R)

Hydraulic Radius, m


zone

caving zone

Fig. 4.12 Caveability assessment using Laubscher‟s chart for studied equivalent continuum properties

(a) RMR; (b) Q - 90% tensile cut-off; (c) Q - 70% tensile cut-off

84

RMR 50 not shown due to excessive fracturing

end of undercutting 4% ore extraction 8% ore extraction 12% ore extraction

RM

R 6

0

RM

R 7

0

RM

R 8

0

Fig. 4.13 Simulation of cave development progression for RMR equivalent continuum properties.

85


Q 0

.67 (

90%

c.o

.)

Q 6

.2 (

90%

c.o

.)

Q 1

7.5

(9

0%

c.o

.)

Q 47.5 not shown due to limited caving

Fig. 4.14 Simulation of cave development progression for Q (90% tensile cut-off) equivalent continuum properties.

86


Q 0

.67 (

70%

c.o

.)

Q 6

.2 (

70%

c.o

.)

Q 1

7.5

(7

0%

c.o

.)


Fig. 4.15 Simulation of cave development progression for Q (70% tensile cut-off) equivalent continuum properties.

87

RMR 50 not shown due to excessive fracturing

RM

R 6

0

RM

R 7

0

RM

R 8

0

Fig. 4.16 Simulation of subsidence development with RMR equivalent continuum properties.

88

90% tensile cut-off 70% tensile cut-off

Q 0

.67

Q 6

.2

Q 1

7.5


Fig. 4.17 Simulation of subsidence development with Q equivalent continuum properties.

89

4.5.4 Conclusions

The following conclusions can be drawn from the conducted modelling study:

neither the RMR nor Q rock mass classification systems can be relied

upon as a robust source of rock mass properties for hybrid FEM/DEM

modelling;

very low estimates of rock mass cohesion and tensile strength derived

using RMR system lead to overestimated susceptibility of simulated rock

mass material to tensile failure, making use of RMR properties

unacceptable for modelling of caving mechanisms;

among all considered Q property sets the properties for the midrange Q

ratings, with an assumed tensile strength of about 1.2 MPa, provide the

most realistic representation of rock mass caveability, cave development

progression and subsidence response;

it appears that the Q properties for the ratings equivalent to RMR 60 to 70

offer generally adequate estimates of deformation modulus, cohesion and

friction, and also, give flexibility in regards to the assumption of the tensile

strength, thus leaving room for response calibration.

Overall, the conducted analysis clearly shows a need for further research into

estimation of rock mass equivalent continuum properties. In the author‟s opinion,

future progress in this area can be achieved through use of the synthetic rock

mass modelling methodology (Pierce et al., 2007) employing PFC and DFN

(discussed in Section 4.3.3). Further work is required to ensure that it can

produce realistic material properties for different rock mass scales and evaluate

its sensitivity to varying stochastic realizations.

4.6 Summary

Among the various methodologies for estimating rock mass equivalent continuum

properties, the use of rock mass classification systems is the most common. The

90

analysis carried out in this chapter evaluated the properties derived from the

RMR, Q and GSI rock mass classification systems. It was found that strength

and deformability characteristics derived using different systems for the same

rating values a show general lack of consistency. Moreover, none of the studied

rock mass classification based correlations offered adequate estimates of all

equivalent continuum rock mass properties. In some instances property values

appear to be excessively conservative. The analysis highlighted the need for

careful examination of rock mass classification properties outputted prior to

acceptance in engineering calculations. A numerical modelling study was carried

out to investigate the applicability of the RMR and the Q based properties

estimates in combined FEM/DEM-DFN modelling of surface subsidence

associated with block caving mining. A novel subsidence modelling approach

was adopted and using cave mining experience-based constraining criteria, such

as caveability, cave propagation and major subsidence damage limits, applicability

of varying property sets was evaluated. Generally it was found that neither RMR

nor Q systems can be relied upon as a robust source of properties for subsidence

modelling. Property estimates for middlerange Q values produced the most

realistic simulated behaviour with respect to the considered constraining criteria.

91

CHAPTER 5: CONCEPTUAL MODELLING STUDY OF THE FACTORS CONTROLLING BLOCK CAVING SUBSIDENCE DEVELOPMENT

5.1 Introduction

In a complex block caving mining environment, subsidence development is a

result of an interplay between several governing factors. Mining experience

suggests that these factors include geological structure (jointing and faults), rock

mass strength, in-situ stress level, mining depth, volume of extracted material and

varying lithological domains. A survey of the literature shows that publications are

limited to a general, qualitative rather than quantitative, description of the influence

of geological structures on the observed subsidence, see Section 2.4. Such

qualitative observations are useful for initial subsidence analysis, however they

require further validation. With regards to other factors, literature sources highlight

their importance but provide only limited further description. Understandably,

discerning the effect of individual factors from field observations is challenging. To

the author‟s knowledge, until now, no comprehensive attempt has been

undertaken to address the fundamental understanding of block caving subsidence

phenomena. This chapter adopts the novel modelling methodology for subsidence

analysis, outlined in Chapter 4, and through a series of conceptual numerical

experiments investigates subsidence development mechanisms and the relative

significance of the factors governing subsidence development.

5.2 Model Setup and Analysis Strategy

The model setup adopted is as described in Section 4.5.1.1. Modelling input

parameters are given in Table 5.1. It should be noted that the rock mass

properties were based on those derived from the Q rock mass classification

system, corresponding to a Q rating of 6.2. Results of the analysis carried out in

92

Section 4.5 illustrated that this property set, with an assumed tensile cut-off of

70%, produced reasonably realistic caving and subsidence development

responses. These properties were further calibrated (through adjustment of

tensile strength) to achieve a better correlation with the constraining criteria. A

tensile cut-off of 75%, corresponding to 1MPa tensile strength, was adopted for

the current modeling. The property set adopted is given in Table 5.1. The

caving behaviour of a rock mass with the assumed properties corresponds to

MRMR ~ 55-60 (i.e. within a typical block caving range of MRMR 30 to 70).

Table 5.1 Modelling input parameters

Parameter Unit Value Parameter Unit Value

Rock mass Discontinuities

Young‟s Modulus, E GPa 18 Fracture cohesion, cf MPa 0

Poisson‟s ratio, 0.25 Fracture friction, f degrees 35

Density, ρ kgm-3 2600 Normal penalty, Pn GPa/m 2

Tensile strength, t MPa 1 Tangential penalty, Pt GPa/m 0.2

Fracture energy, Gf Jm-2 60

Cohesion, ci MPa 4.7 Stress level

Friction, i degrees 45 In-situ stress ratio, K 1

Dilation, ψ degrees 5

The conceptual study modelling presented in this chapter involved more than 500

days of continuous run time on a 3.4GHz, 2GB RAM single processor PC, with an

average run time of individual simulations of about 16 days. Due to limitations of

computational processing time the number of simulations was limited to 36.

Emphasis in the conceptual study modelling has been given to the analysis of the

effect of geological discontinuities, widely recognized as a primary control on block

caving induced surface subsidence.

93

5.3 Influence of Jointing

5.3.1 Effect of Joint Orientation

5.3.1.1 Model Description

The effect of joint orientation was evaluated through comparison of simulations

assuming five different combinations, as summarized in Table 5.2.

Table 5.2 Modelling scenarios for analysis of the effect of joint orientation

Scenario Number of sets

Joint sets dips, °

Description Figure

Base Case Two sets 90/0 Orthogonal sets, vertical/horizontal

5.1(a)

J1 Two sets 80/10 Orthogonal sets, sub-vertical/sub-horizontal

5.1(b)

J2 Two sets 70/20 Orthogonal sets, steeply dipping/gently dipping

5.1(c)

J3 Two sets 70/0 Orthogonal sets, steeply dipping/horizontal

5.1(d)

J4 Three sets 70/20/90 Orthogonal sets, steeply dipping/gently dipping/vertical

5.1(e)

94

0-100 -50-150-200-250 10050 150 200 250 300-300

(a)

BC

(b)

J1

(c)

J2

(d)

J3

(e)

J4

Fig. 5.1 Assumed fracture orientations for BC (a), J1 (b), J2 (c), J3 (d) and J4 (e) models

90°

0°

80°

10°

70°

20°

70°

0°

0°

70°

20°

ore block

W E

95

The Base Case, J1 and J2 models are meant to illustrate how varying orientation

of the same joint pattern affects subsidence development mechanisms and final

subsidence footprint. Models J3 and J4 are based on the J2 model and are used

to evaluate the significance of the change of orientation of the sub-vertical set and

the presence of an additional vertical set, respectively. The Base Case model was

selected as a reference as a combination of vertical and horizontal joints represent

conditions “ideal” for caving.

5.3.1.2 Subsidence Mechanisms

Figs. 5.2 to 5.4 present the mechanism of surface deformation development for

Base Case, J1, J2, J3 and J4 models at 35, 50 and 60% caved ore extraction.

All models show a common subsidence crater formation mechanism which can be

summarized as:

caving/unloading induced fracturing coupled with continuous ore extraction

creates favourable kinematic conditions for detachment of major near

surface rock mass segments adjacent to the caving front;

the detached rock mass segments collapse into the cave through rotational

and/or translation failure; surface expressions of such failure involves

formation and growth of multiple tensile cracks which eventually disappear

as the rock mass disintegrates;

the extreme limits of these detaching segments manifested at the surface

represent the initial subsidence crater walls;

continuous removal of the ore leads to lowering of the rubblized rock within

the crater reducing lateral support to the crater walls promoting further

lateral growth of the subsidence crater through rotational and/or

translational failures of the crater wall segments into the cave.

The described mechanism of subsidence deformation development is in general

agreement with that suggested by Abel & Lee (1980) (see Section 2.2).

96

35% ore extraction 50% ore extraction 60% ore extraction

(a)

BC

(b)

J1

Legend: rotational failure; translational failure; active rock mass movement; developing rock mass failure

Fig. 5.2 Subsidence crater formation for Base Case (a) and J1(b) models

80°

10°

50m

90°

0°

0°

deviation of the center of surface depression with respect to the block centre vertical axis 9°

5°

97

35% ore extraction

50% ore extraction 60% ore extraction

(a)

J2

(b)

J3


Fig. 5.3 Subsidence crater formation for J2 (a) and J3 (b) models

70°

20°

70°

0°

9°

4°


98

35% ore extraction

50% ore extraction 60% ore extraction

J4


Fig. 5.4 Subsidence crater formation for J4 model

Base Case J2

5%

ore

extr

actio

n

Fig. 5.5 Variation of vertical stress (Pa) contours with caving at 5% ore extraction for Base Case and J2 models

20° 0°

70°

1°


99

It can be inferred from Figs. 5.2 to 5.4 that the direction of cave propagation

toward the surface, the location of the cave breakthrough and the mechanisms of

near surface rock mass failure are all strongly controlled by joint orientation. Fig.

5.5 shows the variation of the vertical stress contours at an early stage of ore

extraction for the Base Case and J2 models. It can be inferred from this figure

that the orientation of the sub-vertical/steeply dipping joint set predetermines the

direction of caving induced rock mass unloading and thus the direction of cave

propagation. Comparing the centres of surface depression at 35% ore extraction

for the Base Case (Fig. 5.2(a)), J1 (Fig. 5.2(b)) and J2 (Fig. 5.3(a)) models, it can

be seen that a rotation of the joint pattern skews the direction of cave

propagation away from the block centre vertical axis and cave propagation is

largely controlled by the steeply inclined set. Rotation of the joint pattern by 10°

moves the centre of surface depression by about 4°, reaching 9° for the J2

model. This trend however may be altered depending on the orientation of the

gently dipping set. Comparing models J2 (Fig. 5.3(a)) and J3 (Fig. 5.3(b)) a

change of inclination of the sub-horizontal set from 20° dip to horizontal shifts the

centre of surface depression closer to the block centre vertical axis by 5°, i.e.

more than 50%. Moreover, comparing models J2 (Fig. 5.3(a)) and J4 (Fig. 5.4) it

is evident that the presence of an additional well defined vertical joint set reduces

the significance of the steeply dipping set, so that the centre of initial surface

depression is nearly aligned with the block centre vertical axis.

Joint orientation controls not only the cave propagation direction but also plays a

significant role in the manner the rock mass is mobilized by caving. In order to

characterize rock mass mobilization development in Figs. 5.2 to 5.4, zones of

active rock mass movement and developing rock mass failure are delineated.

Within the former zone the rock mass is fully disintegrated and the latter zone

indicates the damaged and potentially unstable rock mass. Figs. 5.2(a) and 5.4

show that the effect of the vertical joint set is relatively limited and the extent of

the rock mass mobilized during initial stages of caving and ore extraction is

largely symmetrical, with respect to the ore block centre axis. As evident from

Figs. 5.2(b) and 5.3, simulations with sub-vertical and steeply dipping sets result

100

in a larger extent of mobilized rock mass. Failure asymmetry with respect to the

block centre vertical axis can be clearly observed, a larger failure is evident in a

zone where sub-vertical/steeply dipping joints are inclined towards the cave

(west of the block centre vertical axis) and more limited failure is observed where

these joints dip towards the cave (east of the block centre vertical axis). This

asymmetry can be attributed to the varying mechanisms of failure of the rock

mass which is governed by the inclination of the vertical/steeply dipping joints.

West of the block centre vertical axis, inclination of the joint sets favours rock

mass failure through flexural and block-flexural toppling, coupled with inclined

cave propagation this creates suitable kinematic conditions for toppling of

massive rock mass segments. In the eastwards direction, a sub-vertical/steeply

dipping joint set creates favourable conditions for sliding and, in combination with

an orthogonal joint set promotes slide toe toppling. Such a failure does not

appear to exceed the dip angle of the sub-vertical joint set, hence limiting the

extent of the mobilized rock mass.

5.3.1.3 Subsidence Topography

Final subsidence deformation and resultant surface profiles at 100% ore

extraction for the Base Case, J1, J2, J3 and J4 models are shown in Figs. 5.6

and 5.7, respectively. It can be clearly seen from these figures that the rock

mass deformation and the surface depression formed due to caving vary quite

significantly depending on the assumed joint orientation. Rotation of the joint

pattern shifts the centre of the surface depression, positioned at the block

centre vertical axis for Base Case model, in a direction opposite to that of

surface asymmetry (i.e. eastwards) and also results in a shallower subsidence

crater. Rotation of the jointing pattern by 10° results in a decrease of the

maximum depth of the crater by about 10%. The maximum crater depth was

observed for the model with vertical/horizontal joint sets (Base Case) and the

minimum for the simulation with steeply dipping/horizontal joint sets (J3). Models

with different joint orientation exhibit varying subsidence crater topography.

101

0-100 -50-150-200-250 10050 150 200 250 300-300

(a)

BC

(b)

J1

(c)

J2

(d)

J3

(e)

J4

Fig. 5.6 Subsidence at 100% ore extraction for BC (a), J1 (b), J2 (c), J3 (d) & J4 (e) models

90°

0°

80°

10°

70°

20°

70°

0°

0°

70°

20°

10cm displ. contours vertical

horizontal

Legend:

angle of fracture initiation

71°

70°

53°

61°

59°

71°

76°

73°

74°

74°

72°

MRV = 28114m3

AI = 0.93

MRV = 30762m3

AI = 0.96

MRV = 34990m3

AI = 0.72

MRV = 35250m3

AI = 0.82

MRV = 30836m3

AI = 0.82

102

-80

-70

-60

-50

-40

-30

-20

-10

0

-350 -250 -150 -50 50 150 250 350

Vert

ical d

isp

lacem

en

ts,

m

Distance from block centre, m

Base case

J1

J2

J3

J4

0, -55

9.4, -49.6

28.6, -41

9.4, -44.5

10, -50

Lowest point coordinates, m

Fig. 5.7 Surface profiles at the end of ore extraction for BC, J1, J2, J3 and J4 models

For the Base Case model a distinct, nearly symmetrical stepped V-shaped crater

is formed. In contrast, for simulations with inclined joints (J1 to J3) the

subsidence crater is asymmetrical. In the direction of maximum asymmetry (i.e.

westwards) the surface subsides without forming major steps, aside from the

crater wall. It is interesting to note that the addition of the vertical joint set in

model J4 reduced crater asymmetry and resulted in a stepped crater topography.

5.3.1.4 Characterization of Major Displacements

In order to quantify the extent of major surface subsidence deformation a 10cm

displacement threshold is adopted. It is assumed that this threshold limits the

zone of major surface disturbance. Fig. 5.6 shows contours of 10cm vertical and

horizontal displacements at 100% ore extraction for Base Case, J1, J2, J3 and

J4 models. Using these contours we can evaluate the mobilized rock mass

volume (MRV), as indicated in the figure. The maximum span of the major

surface displacement induced by the caving is delineated using angular limits, or

angles of fracture initiation according to subsidence characterization terminology

proposed by van As (2003). Comparing angles limiting major surface

deformations for the presented models, it can be seen that in an eastward

direction from the block centre vertical axis all models show consistently steep

limiting angles ranging from 72° to 76°. In a westward direction, dissimilarity in

the limiting angles between the different models is apparent. The lowest

103

minimum angle of fracture initiation of 53° is observed for model J2 (Fig. 5.6(c))

and the highest angle of 71° for the Base Case model (Fig. 5.6(a)), i.e. rotation of

the joint pattern by 20° results in the increase of subsidence limits in the sub-

vertical set dip direction by about 20%. Interestingly, the initially asymmetrical

subsidence development for model J1 with a 10° joint pattern rotation (see Fig.

5.6(b)) eventually becomes more symmetrical, and only a minor increase in the

limiting angle is observed. It appears that the 80° dip of the sub-vertical set is

insufficient to cause extensive flexural toppling. Model J4 (Fig. 5.6(e)) yields the

second lowest angle of fracture initiation of 61° which is about 10% lower than for

J2 model. This indicates that the vertical joint set, by providing additional planes

of weakness, limits the extent of rock mass mobilized by the caving. It is

interesting to note that initial subsidence development for the J4 model was

nearly symmetrical, as shown in Fig. 5.4. Subsidence asymmetry in the

westwards direction began to develop as the constraining effect of the rubblized

rock was diminished due to continuous ore extraction, allowing block toppling

and sliding of the crater wall segments along the gently dipping joint set.

Comparing models J2 and J3 it can be concluded that decreasing the dip of the

gently dipping set by 20° increases the limiting angle by 10° or about 20%. Such

an influence can tentatively be explained by reduction of the potential for rotation

and sliding towards the cave along the gently dipping joint set.

To characterize subsidence asymmetry a block cave subsidence parameter,

asymmetry index, AI, is introduced. This index is defined as the ratio of the

minimum to maximum angles delineating the extent of major (≥10cm) surface

displacements, as shown in Fig. 5.6. Perfect symmetry corresponds to an

asymmetry index of 1.

In addition to using the limiting angles, shown in Fig. 5.6, the zone of major

surface deformation can be further characterized by its total extent and relative

significance with respect to the vertical axis of the block, as shown in Fig. 5.8.

According to Fig. 5.8(a) and (b), changes in the joint set orientation causes an

increase in the extent of the total major surface deformations by up to 30% and

41% for major vertical and horizontal surface displacements, respectively. For all

104

models the total extent of the major surface horizontal deformation is consistently

larger than or equal to the extent of vertical displacements. According to Fig.

5.8(c) and (d) depending on the joint orientation assumption:

west of the block centre vertical axis the extent of major surface

deformations increases up to a maximum of about 40% and 70% for

vertical and horizontal displacements;

east of the block centre vertical axis only a moderate increase of up to

20% for both vertical and horizontal displacements is observed.

207234

268 269245

100%

113%

129%

130%

118%

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

To

tal exte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts

no

rmalized

b

y B

ase C

ase, %

To

tal e

xte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts,

m

BC J1 J2 J3 J4

218235

308

269290

100%

108% 141%

123%

133%

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

To

tal exte

nt o

f 10cm

ho

riz.

su

rface d

isp

lacem

en

ts

no

rmalized

b

y B

ase C

ase, %

To

tal e

xte

nt o

f 10cm

ho

riz.

su

rface d

isp

lacem

en

ts,

m

BC J1 J2 J3 J4

-112

95

-123

111

-161

107

-161

108

-132

113119%

132%

114%

144%

113%

144%

117%

110%

100%

100%

-300 -200 -100 0 100 200 300

-250 -200 -150 -100 -50 0 50 100 150 200 250

Extent of 10cm surface vertical displacements in relation to block centre, normalized by Base Case, %

Extent of 10cm surface vertical dispacements in relation to block centre, m

BCJ1J2J3J4

BCJ1J2J3J4

-118

100

-123

112

-201

107

-161

108

-173

117117%

147%

108%

136%

107%

170%

116%

104%

100%

100%

-300 -200 -100 0 100 200 300

-250 -200 -150 -100 -50 0 50 100 150 200 250

Extent of 10cm surface horizontal displacements in relation to block centre, normalized by Base Case, %

Extent of 10cm surface horizontal displacements in relation to block centre, m

BCJ1J2J3J4

BCJ1J2J3J4

Fig. 5.8 Subsidence characterization for Base Case, J1, J2, J3 and J4 models Total extent of 10cm vertical (a) and horiz. (b) surface displacements; extent of 10cm surface vertical (c) and horiz. (d) displacements in relation to centre axis of the block, in m

Evolution of the zones of major (≥10cm) surface deformation with continuous ore

extraction and the rate of their growth west of the block centre vertical axis for

Base Case, J1, J2, J3 and J4 models is shown in Figs. 5.9 and 5.10,

respectively. From these figures it can be inferred that for all considered models

major subsidence deformation develop in a relatively rapid manner reflecting quick

mobilization of the massive rock mass segments. Fig. 5.10(a) shows that for the

majority of the models, with the exception of model J4, about 90% of the

(a) (b)

(c) (d)

105

maximum vertical deformations is achieved by 50% ore extraction. Model J4

exhibits a more subtle trend in vertical deformation development which can be

attributed to the previously discussed gradual block toppling failure mechanism.

Horizontal deformation development trends are presented in Fig. 5.10(b), which

indicates that for simulations which involve flexural toppling failure, models J1,

J2, and J3, horizontal displacements generally develop at a rate of up to 80%

greater than the vertical displacements.

0

10

20

30

40

50

60

70

80

90

100

-250 -200 -150 -100 -50 0 50 100 150 200 250

Ore

extr

acti

on

, %

Extent of 10cm surface deformations, m

YY

XX

0

10

20

30

40

50

60

70

80

90

100

-250 -200 -150 -100 -50 0 50 100 150 200 250

Ore

extr

acti

on

, %


YY

XX

Fig. 5.9 Evolution of zone of major (≥10cm) vertical (YY) and horizontal (XX) surface deformations with continuous ore extraction for Base Case (a), J1 (b), J2 (c), J3 (d) and J4 (e) models

0

10

20

30

40

50

60

70

80

90

100

-250 -200 -150 -100 -50 0 50 100 150 200 250

Ore

extr

acti

on

, %


YY

XX

0

10

20

30

40

50

60

70

80

90

100

-250 -200 -150 -100 -50 0 50 100 150 200 250

Ore

extr

acti

on

, %


YY

XX

0

10

20

30

40

50

60

70

80

90

100

-250 -200 -150 -100 -50 0 50 100 150 200 250

Ore

extr

acti

on

, %


YY

XX

(d) J3

(e) J4

(b) J1 (a) BC

(c) J2

106

Fig. 5.10 Rate of growth of 10cm surface displacement zone west of the block centre vertical axis with continuous ore extraction for Base Case, J1, J2, J3 and J4 models (a) vertical displacements, (b) horizontal displacements

5.3.1.5 Characterization of Far-Field Displacements

When considering the location of mine infrastructure it is important to appreciate the

magnitude of surface displacements at specific distances from the area of imminent

failure (caving boundary and its immediate vicinity). Fig. 5.11 shows total vertical and

horizontal displacements at the end of ore extraction at 300, 250, 200 and 150m

distances from the block centre for Base Case, J1, J2, J3 and J4 models.

J2 J3

J4

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

-300 -250 -200 -150 150 200 250 300

Vert

ical d

isp

lacem

en

ts,

m


-0.38 -2.1

J2

J3

BC

BC BC

J1

J1

J1J2

J2

J2

J2

J3

J3

J3

J3

J4

J4

J4

0

0.05

0.1

0.15

0.2

0.25

0.3

-300 -250 -200 -150 150 200 250 300

Ho

rizo

nta

l dis

pla

cem

en

ts, m


0.9 3.8

Fig. 5.11 Total vertical (a) and horizontal (b) surface displacements at the end of ore extraction at different distances from block centre for Base Case, J1, J2, J3 and J4 models

0

20

40

60

80

100

120

0 20 40 60 80 100 120

exte

nt

of

vert

ical

10cm

su

rface

dis

pla

cem

en

ts,

%

Ore extraction, %

BC_YY

J1_YY

J2_YY

J3_YY

J4_YY

0

20

40

60

80

100

120

0 20 40 60 80 100 120

exte

nt

of

ho

rizo

nta

l 10cm

su

rface

dis

pla

cem

en

ts,

%

Ore extraction, %

BC_XX

J1_XX

J2_XX

J3_XX

J4_XX

(b) (a)

(a)

(b)

107

According to this figure the least amount of surface displacements is exhibited by

the Base Case model (90°/0°), so that only minor horizontal displacements of

about 1cm are observed 100m from the caving boundaries (150m from the block

centre vertical axis). The largest magnitude of displacement are observed for the

J2 (70°/20°) and J3 (70°/0°) models, where 1cm horizontal displacements are

noted as far as 200m west of the caving boundaries. Far-field surface

displacements generally mirror the trends observed for the major surface

deformations, showing strong asymmetry in the dip direction of the sub-

vertical/gently dipping joint sets. Apparently, the magnitude of accumulated

surface displacement as well as its extent will depend on the mechanism of the

rock mass failure induced by caving, which, as discussed earlier is strongly

controlled by the joint orientation. Comparing vertical (Fig. 5.11(a)) and

horizontal (Fig. 5.11(b)) far-field displacements, it can be seen that in the studied

models there is a clear trend of higher far-field horizontal displacements. This

trend is in agreement with the measurements of caving induced surficial

displacements at Lakeshore mine, as reported by Panek (1984).

5.3.1.6 Conclusions

Based on the results of ELFEN modelling, the following can be concluded with

respect to the effect of joint orientation on caving induced surface subsidence

development and the resultant deformation footprint:

1. Well defined, persistent, vertical to steeply dipping joints govern the

direction of cave propagation and the mechanism of near surface rock

mass mobilization. The shallower the dip of these joints the more inclined

from vertical the cave propagation direction is and the more asymmetrical

the surface deformation is with respect to the block centre vertical axis. In

cases where multiple well defined and persistent steeply dipping sets are

present, the steepest set will generally have the predominant influence.

2. Modelling results in part confirm observations of Crane (1929) and Wilson

(1958) who noted that in the absence of major geological discontinuities

subsidence deformations are controlled by the joint dip.

108

3. Major subsidence asymmetry is observed in the dip direction of the sub-

vertical/steeply dipping set. Where joints are inclined towards the cave, the

rock mass fails through a combination of block-flexural and block toppling

and the detachment and sliding of major rock segments, which is in

agreement with the conceptual caving failure model proposed by Hoek

(1974). Where a sub-vertical joint set is dipping into the cave, the surface

deformation direction is controlled by the dip of the sub-vertical joint set. In

this case the rock mass fails predominantly through block toppling and

sliding along the sub-vertical joints.

4. The orientation of well defined, persistent, gently dipping joints influences

the extent of the rock mass mobilized by the failure and the degree of

subsidence asymmetry.

5.3.2 Effect of Joint Persistence

The effect of joint persistence on block caving induced surface subsidence

development was evaluated using the J2 (70°/20°) model, which yielded the

maximum subsidence deformation. Two scenarios were considered:

I. J5, where 25% higher persistence was assumed for all joints

II. J6, where 25% lower persistence was assumed for all joints

A series of Excel based macros were developed to process the FracMan output

file and evenly adjust the DFN based fracture length according to a specified

percentage value.

Figs. 5.12(a) and (b) illustrate surface subsidence deformations at 100% ore

extraction for the J5 and J6 models, respectively. Comparing these models

with model J2 (Fig. 5.6(c)) it can clearly be seen that an increase in joint

persistence by 25% results in a larger extent of the rock mass mobilized by

caving in the dip direction of the steeply dipping set. The minimum limiting

angle delineating major (≥10cm) surface deformations decreases from 53° to

47° degrees. A reduction in joint persistence by 25% limits the extent of rock

mass mobilization and an increase in the limiting angle from 53° to 71°.

109

0-100 -50-150-200-250 10050 150 200 250 300-300

(a)

J5

(b)

J6

Fig. 5.12 Subsidence at 100% ore extraction for J5 (a) and J6 (b) models

Comparing the extent of major rock mass deformation for models J2, J5 and J6,

Fig. 5.13, shows a well defined trend of an increasing zone of influence with

increasing joint persistence. A 50% change in joint persistence between

models J6 and J5 results in an increase in the total extent of the major vertical

and horizontal surface displacements of about 50% and 60% respectively. This

may be attributed to the varying degree of blockiness of the rock mass

depending on joint persistence. Higher joint persistence contributes to a higher

rock mass blockiness, and given a favourable joint orientation leads to

increased kinematic susceptibility of the rock mass to toppling failure. A

decrease in joint persistence reduces the blockiness of the rock mass and its

kinematic susceptibility to failure. This leads to a lower rock mass mobilization

due to the formation of more rock bridges.

70°

20°

70°

20°

persistence (+)25%

persistence (-)25%

47°

71°


horizontal

Legend:


47°

73°

76°

MRV = 42076m3

AI = 0.64

MRV = 32358m3

AI = 0.93

110

222

268

331

83%

100%

124%

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

To

tal e

xte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts

no

rmalized

by J

2, %

To

tal e

xte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts,

m

J6 J2 J5

222

308350

72%

100%

114%

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

To

tal e

xte

nt o

f 10cm

ho

riz.

su

rface d

isp

lacem

en

ts

no

rmalized

by J

2, %

To

tal e

xte

nt o

f 10cm

ho

riz.

su

rface d

isp

lacem

en

ts,

m

J6 J2 J5

-121

101

-161

107

-219

112105%

136%

100%

100%

94%

75%

-300 -200 -100 0 100 200 300

-250 -200 -150 -100 -50 0 50 100 150 200 250

Extent of 10cm surface vertical displacements in relation to block centre, normalized by J2, %


J6

J2

J5

J6

J2

J5

-121

101

-201

107

-237

113106%

118%

100%

100%

94%

60%

-300 -200 -100 0 100 200 300

-250 -200 -150 -100 -50 0 50 100 150 200 250

Extent of 10cm surface horizontal displacements in relation to block centre, normalized by J2, %


J6

J2

J5

J6

J2

J5

Fig. 5.13 Subsidence characterization for J2, J5 and J6 models Total extent of 10cm vertical (a) and horiz. (b) surface displacements; extent of 10cm surface vertical (c) and horiz. (d) displacements in relation to centre axis of the block, in m

J6

J2

J5

J5

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

-300 -250 -200 -150 150 200 250 300

Vert

ical d

isp

lacem

en

ts,

m


-0.38

J5

-0.47

J2

J6 J

6

J6

J6J2

J2

J2

J5

J5 J5

0

0.05

0.1

0.15

0.2

0.25

0.3

-300 -250 -200 -150 150 200 250 300

Ho

rizo

nta

l d

isp

lacem

en

ts, m


1.60.4 0.9

Fig. 5.14 Total vertical (a) and horizontal (b) surface displacements at the end of ore extraction at different distances from block centre for J2, J5 and J6 models

(a) (b)

(c) (d)

(a)

(b)

111

According to Fig. 5.14, the larger rock mass mobilization associated with higher

joint persistent leads to significantly larger far-field surface displacements west

of the block centre vertical axis.

The results of the modelling show that joint persistence may have a very

significant effect on surface subsidence induced by block caving. It should

however be recognized that the effect of joint persistence will be a function of the

joint inclination. Considering the fact that models assuming vertical/horizontal

joint sets resulted in nearly symmetrical cave development it is unlikely the higher

joint persistence will significantly affect subsidence development in such settings.

Conversely steeply to gently dipping highly persistent joint sets dipping into the

caving front may create favourable conditions for translational and rotational

failure, reducing considerably the shearing resistance of the rock mass.

5.3.3 Effect of Joint Shear and Normal Stiffness

The effect of joint contact properties was evaluated assuming a 500% higher

normal and shear stiffness properties on pre-inserted fracture interfaces. Two

scenarios were considered based on the Base Case (90°/0°) and J2 (70°/20°)

models:

I. J7 (90°/0°; normal stiffness 10GPa/m, shear stiffness 1GPa/m)

II. J8 (70°/20°; normal stiffness 10GPa/m, shear stiffness 1GPa/m)

Comparing caving induced subsidence deformation for the Base Case (Fig.

5.6(a)) and J7 (Fig. 5.15(a)) models, it can be seen that for the scenarios with

vertical/horizontal joints an increase in joint stiffness resulted in a relatively minor

decrease in subsidence damage. According to Fig. 5.16(a) and (b) the total

extent of major (≥10cm) surface deformations was reduced by up to 9%. No

noticeable difference was observed in the magnitude of far-field surface

displacements, see Fig. 5.17.

112

0-100 -50-150-200-250 10050 150 200 250 300-300

(a)

J7

(b)

J8

Fig. 5.15 Subsidence at 100% ore extraction for J7 and J8 model

207188

268254

100%

91%

100%

95%

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

To

tal e

xte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts

no

rmalized

by B

C/J

2, %

To

tal e

xte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts,

m

BC J7 J2 J8

218202

308281

100%

93%

100%

91%

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

To

tal e

xte

nt o

f 10cm

ho

riz.

su

rface d

isp

lacem

en

ts

no

rmalized

by B

C/J

2, %

To

tal e

xte

nt o

f 10cm

ho

riz.

su

rface d

isp

lacem

en

ts,

m

BC J7 J2 J8

-112

95

-102

86

-161

107

-126

128120%

78%

100%

100%

91%

91%

100%

100%

-300 -200 -100 0 100 200 300

-250 -200 -150 -100 -50 0 50 100 150 200 250

Extent of 10cm surface vertical displacements in relation to block centre, normalized by BC/J2, %


BC

J7

J2

J8

BC

J7

J2

J8

-118

100

-102

100

-201

107

-153

128120%

76%

100%

100%

100%

86%

100%

100%

-300 -200 -100 0 100 200 300

-250 -200 -150 -100 -50 0 50 100 150 200 250

Extent of 10cm surface horizontal displacements in relation to block centre, normalized by BC/J2, %


BC

J7

J2

J8

BC

J7

J2

J8

Fig. 5.16 Subsidence characterization for Base Case, J7, J2 and J8 models Total extent of 10cm vertical (a) and horiz. (b) surface displacements; extent of 10cm surface vertical (c) and horiz. (d) displacements in relation to centre axis of the block, in m

70°

20°

90°

0°

75°

63°


horizontal

Legend:


75°

76°

69°

(a) (b)

(c) (d)

joints stiffnesses (+)500%

joints stiffnesses (+)500%

MRV = 28043m3

AI = 0.99

MRV = 33324m3

AI = 0.91

113

J2 J8

J8

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

-300 -250 -200 -150 150 200 250 300

Vert

ical d

isp

lacem

en

ts,

m


-0.38

J7

BC BC

J7 J7J2

J2

J2

J2

J8

J8

0

0.05

0.1

0.15

0.2

0.25

0.3

-300 -250 -200 -150 150 200 250 300

Ho

rizo

nta

l d

isp

lacem

en

ts, m


0.9

Fig. 5.17 Total vertical (a) and horizontal (b) surface displacements at the end of ore extraction at different distances from block centre for Base Case, J1, J2, J3 and J4 models

A more pronounced influence of the higher joint stiffnesses is observed for model J8

with inclined joints. As observed in Fig. 5.6(c) and 5.15(b), an increase in joint

stiffness by 500% increases the minimum angle limiting major surface deformations

by about 15%, from 53 to 63 , thus reducing subsidence asymmetry. It is interesting

to note that in the direction of major subsidence asymmetry (westward) the extent of

the horizontal displacements was reduced by a larger margin (7%) than for vertical

displacements, see Fig. 5.16 (c) and (d). Comparison of the far-field surface

displacement magnitudes for models J2 and J7, Fig. 5.17, shows a significant

reduction in surface displacements for the model with higher stiffnesses (J7).

Overall, the results of ELFEN modelling infer that for gently to steeply inclined

joint sets dipping into the caving front, joint contact stiffness properties will affect

the degree of rock mass resistance to failure and therefore influence the resultant

surface subsidence. It appears that this influence is moderate and will

predominantly be controlled by the joint‟s resistance to shear, i.e. by the shear

stiffness and shear strength. For the joint sets with vertical to sub-vertical and

horizontal to sub-horizontal dip the influence of joint stiffnesses on the resultant

subsidence is of a lesser significance.

(a)

(b)

114

5.4 Influence of Faults

The influence of faults on surface subsidence development was evaluated

through a series of models assuming a fault that dips toward the cave,

considering different fault locations with respect to the block centre vertical axis

and varying the fault inclination. To allow comparison of induced subsidence

these preliminary analyses assumed the contact properties on fault interfaces

to be identical to the contact characteristics of pre-inserted discontinuities

(shown in Table 5.1). Two different jointing conditions, the Base Case (90°/ 0°)

and J2 (70°/ 20°), were employed.

5.4.1 Effect of Fault Location

The effect of fault location on surface subsidence development was evaluated

based on five scenarios, Table 5.3.

Table 5.3 Modelling scenarios for analysis of the effect of fault location

Scenario Joint sets dips, ° Fault dip, ° Fault location, m Figure

F1

90/0

60

50 5.18(a)

F2 100 5.18(b)

F3 150 5.18(c)

F4 70/20

100 5.18(d)

F5 150 5.18(e)

Figs. 5.19 to 5.23 illustrate the mechanisms of surface subsidence development at

35, 50 and 60% ore extraction and Fig. 5.24(a,b,c) shows resultant subsidence

deformations at 100% ore extraction for models employing vertical/horizontal joints

(F1, F2, F3). Comparing these models it can be seen that depending on the

location of the fault the degree of its influence on caving induced surface

subsidence will vary. For the model with a fault located at 50m from the block

centre vertical axis (F1, Figs. 5.19 and 5.22(a)), caving induced unloading quickly

triggers translational failure and full disintegration of the fault hanging wall and a

gradual failure of the fault footwall. By the end of ore extraction the fault is almost

fully consumed by the caving. Observed surface subsidence deformations are

largely symmetrical with respect to the block centre vertical axis.

115

0-100 -50-150-200-250 10050 150 200 250 300-300

(a) F1

(b) F2

(c) F4

(d) F3

(e) F5

(f) F6

(g) F8

(h) F7

(i) F9

Fig. 5.18 Assumed fracture orientations and fault positions for F1 to F9 models

90°

0°

70°

20°

90°

0°

70°

20°

90°

0°

90°

0°

70°

20°

90°

0°

70°

20°

fault

60°

50m

60°

100m

60°

150m

45°

75°

116

35% ore extraction

50% ore extraction

60% ore extraction

Legend: rotational failure; translational failure; fault location prior to failure

active rock mass movement; developing rock mass failure

Fig. 5.19 Subsidence crater formation for F1 model

50m

90°

0°

117

35% ore extraction

50% ore extraction

60% ore extraction




50m

90°

0°

118

35% ore extraction

50% ore extraction

60% ore extraction

Legend: rotational failure;



50m

90°

0°

119

35% ore extraction

50% ore extraction

60% ore extraction




70°

20°

50m

120

35% ore extraction

50% ore extraction

60% ore extraction

Legend: rotational failure; translational failure;



70°

20°

50m

121

0-100 -50-150-200-250 10050 150 200 250 300-300

(a)

F1

(b)

F2

(c)

F3

(d)

F4

(e)

F5

Fig. 5.24 Subsidence at 100% ore extraction for F1, F2, F3, F4 and F5 model

90°

0°

70°

20°

70°

20°

90°

0°

90°

0°

fault location prior to caving

73°

61°

73°

61°

59°

10cm displ. contours

vertical

horizontal

Legend:


73°

73°

76°

74°

74°

74°

MRV = 30154m3

AI = 1.0

MRV = 32207m3

AI = 0.80

MRV = 27519m3

AI = 0.99

MRV = 34630m3

AI = 0.82

MRV = 35602m3

AI = 0.80

122

The minimum angle delineating the extent of major ( 10cm) surface

displacements is 73°, which is only 2° higher than for the same model but without

a fault (Base Case, Fig. 5.6(a)). For the model with a fault located 100m from the

block centre vertical axis (F2, Fig. 5.20) a notably different subsidence

development mechanism is observed. Only a minor undercuting of the fault

coupled with caving induced unloading triggered translational failure of major

hanging wall segments along the fault interface, eventually resulting in the

hanging wall “sagging” into the cave. The fault footwall withstood the caving and

sustained only minor damage. Surface subsidence deformations are clearly

asymmetrical in a direction towards the fault. The minimum angle delineating the

extent of major surface displacements is 61°, which is 10° less than for the Base

Case model. A fault positioned outside the caving boundaries, at 150m from the

block centre vertical axis (F3, Fig. 5.21), did not exhibit any significant influence

on surface subsidence development. As seen in Fig. 5.25 the presence of a

steeply dipping fault, in a vertical/horizontal jointed rock mass, located at 50 (F1)

and 150m (F3) from the block centre vertical axis had negligible effect on the

extent of the zone of major surface displacements. In contrast, a fault located at

100m (F2) increased the extent of major vertical and horizontal displacements

zone by about 20%, primarily towards the fault.

Subsidence development mechanisms for F4 and F5 models, in which

steeply/gently dipping (70°/20°) joints were assumed, are illustrated in Figs. 5.22

and 5.23 and show similar observed trends as previously discussed for the F2

and F3 models. Final surface subsidence deformations at 100% ore extraction

for models F4 and F5 are given in Fig. 5.24(d,e). Comparing the models, where

a fault is intersecting the block (F2, F4), it can be noted that the change of joint

orientation did not affect the extent of major surface deformation, which was

limited by the fault. For models, where the fault does not intersect the block (F3,

F5), subsidence deformations were primarily governed by jointing. Comparing

the F3 (Fig. 5.24(c)) and Base Case (Fig. 5.6(a)) models, increased tensile

fracturing can be noted in the hanging wall in the vicinity of the caving boundary

indicating the weakening effect of the fault on the hanging wall rock mass.

123

Comparison of J2 (Fig. 5.6(c)) and F5 (Fig. 5.24(e)) models illustrates the limiting

effect of the fault on rock mass mobilization. It appears that the fault prevented

mobilization of a rock mass in the footwall, increasing the limiting angle from 53°

to 59°. According to Fig. 5.26 the presence of a fault in steeply/gently dipping

(70°/20°) joint settings located at 100 and 150m from the block centre vertical

axis decreased the zone of major surface horizontal displacements by 17% and

13%, respectively, in the direction towards the fault.

Figs. 5.27 and 5.28 illustrate far-field displacements for models based on

vertical/horizontal and inclined joints, respectively. For models with

vertical/horizontal joints, faults generally increased the magnitude and extent of

the far-field displacements. The largest increase was observed for the model

with a fault located 150m from the block centre vertical axis (F3), where

horizontal displacements in excess of 1cm were observed as far as 200m from

the caving boundary, which is twice as far as for the model without a fault (Base

case). For models with inclined joints the opposite trend was observed, the

presence of a fault limited both the magnitude and extent of far-field

displacements. Irrespective of jointing orientation horizontal displacements were

predominantly observed.

Caving induced unloading of the hanging wall results in a formation of a

topographical step where the fault daylights. Fig. 5.29 compares differential XY

displacements along fault surfaces with continuous ore extraction for all studied

models. Depending on the fault location with respect to the block centre

movements at the fault surface may vary significantly. For the models F1, F2

and F4, where a fault intersects the block, movements on the order of metres

were observed, whereas for models F3 and F5, where a fault did not intersect the

block, movements of up to several centimetres were noted. Inclination of the

joints affects these movements, such that larger XY displacements, which

develop more rapidly, are observed for models with inclined joints.

124

207 202

255

212

100%

98% 123%

102%

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

To

tal e

xte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts

no

rmalized

by B

ase C

ase, %

To

tal e

xte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts,

m

BC F1 F2 F3

218 220

258

220

100%

101%

118%

101%

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

To

tal e

xte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts

no

rmalized

by B

ase C

ase, %

To

tal exte

nt o

f 10cm

ho

riz.

su

rface d

isp

lacem

en

ts,

m

BC F1 F2 F3

-112

95

-110

92

-160

95

-112

100105%

100%

100%

143%

97%

98%

100%

100%

-300 -200 -100 0 100 200 300

-250 -200 -150 -100 -50 0 50 100 150 200 250



BC

F1

F2

F3

BC

F1

F2

F3

-118

100

-110

110

-160

98

-112

108108%

95%

98%

136%

110%

93%

100%

100%

-300 -200 -100 0 100 200 300

-250 -200 -150 -100 -50 0 50 100 150 200 250



BC

F1

F2

F3

BC

F1

F2

F3

Fig. 5.25 Subsidence characterization for Base case, F1, F2 and F3 Total extent of major (≥10cm) vertical (a) and horizontal (b) surface displacements in m and in % of Base case value; extent of 10cm surface vertical (c) and horizontal (d) displacements in relation to centre axis of the block, in m

268 269 275

100%

100%

103%

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

To

tal exte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts

no

rmalized

b

y J

2, %

To

tal e

xte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts,

m

J2 F4 F5

308

268

279

100%

87%

91%

0

50

100

150

200

250

300

350

240

250

260

270

280

290

300

310

320

To

tal exte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts

no

rmalized

b

y J

2, %

To

tal exte

nt o

f 10cm

ho

riz.

su

rface d

isp

lacem

en

ts,

m

J2 F4 F5

-161

107

-161

108

-167

108101%

104%

101%

100%

100%

100%

-300 -200 -100 0 100 200 300

-250 -200 -150 -100 -50 0 50 100 150 200 250



J2

F4

F5

J2

F4

F5

-201

107

-160

108

-171

108101%

85%

101%

80%

100%

100%

-300 -200 -100 0 100 200 300

-250 -200 -150 -100 -50 0 50 100 150 200 250



J2

F4

F5

J2

F4

F5

Fig. 5.26 Subsidence characterization for J2, F4 and F5 Total extent of major (≥10cm) vertical (a) and horizontal (b) surface displacements in m and in % of J2 value; extent of 10cm surface vertical (c) and horizontal (d) displacements in relation to central axis of the block, in m

(a) (b)

(c) (d)

(a) (b)

(c) (d)

125

F3

F3

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

-300 -250 -200 -150 150 200 250 300

Vert

ical d

isp

lacem

en

ts,

m


-2

F2

BC BCF

1

F1

F1

F2

F2

F3 F3

F3

F3

0

0.05

0.1

0.15

0.2

0.25

0.3

-300 -250 -200 -150 150 200 250 300

Ho

rizo

nta

l dis

pla

cem

en

ts, m


1.2

Fig. 5.27 Total vertical (a) and horizontal (b) surface displacements at the end of ore extraction at different distances from block centre for Base Case, F1, F2 and F3 models

J2

J2

F4

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

-300 -250 -200 -150 150 200 250 300

Vert

ical d

isp

lacem

en

ts,

m


-0.4

F5

-3.2

J2

J2

J2

J2F4

F4

F4F5

F5

F5

0

0.05

0.1

0.15

0.2

0.25

0.3

-300 -250 -200 -150 150 200 250 300

Ho

rizo

nta

l d

isp

lacem

en

ts, m


1.20.8

Fig. 5.28 Total vertical (a) and horizontal (b) surface displacements at the end of ore extraction at different distances from block centre for J2, F4 and F5 models

(a)

(b)

(a)

(b)

126

Fig. 5.29 Differential XY displacements for surface points on the fault hanging and footwalls: (a) F1, F2 and F3; (b) F4 and F5 models

Overall, the ELFEN models demonstrated that the location of the fault may play

an important role in defining the extent of surface subsidence deformation:

1. It appears that steeply dipping faults, daylighting into the cave and located

within an area of imminent caving are likely to be caved and are unlikely to

play any major role in the resultant subsidence.

2. Faults partially intersecting the caving area may create favourable

conditions for failure of the entire hanging wall.

3. Depending on rock mass fabric, faults located in the vicinity of the caving zone

may have a minimal influence or decrease the extent of the area of subsidence

deformation. The former behaviour was observed for horizontal/vertical joint

settings and the latter for orthogonal steeply/gently dipping joints. It should be

recognized that current modelling did consider placing the fault on the east

side of the model where it would be closely aligned with steeply dipping joints.

It appears that in this case the fault could extend the zone of influence.

4. A topographical step in the surface profile is formed where the fault

daylights at the surface. Significant movements should be anticipated if

the fault daylights into the cave.

footwall

hanging

wall

differential

XY displacement

-4.31m

-2.37m

-0.02m

-5

-4

-3

-2

-1

0

0 10 20 30 40 50 60 70 80 90 100

Dif

fere

nti

al

XY

d

isp

lac

em

en

ts, m

Ore extraction, %

F1

F2

F3

-3.73m

-5

-4

-3

-2

-1

0

0 10 20 30 40 50 60 70 80 90 100

Dif

fere

nti

al

XY

d

isp

lac

em

en

ts, m

Ore extraction, %

F4

F5

-0.07m

hangingwall disintegrated

(b)

(a)

90°

0°

70°

20°

127

5.4.2 Effect of Fault Inclination

The effect of fault inclination on surface subsidence development was evaluated

based on six modelling scenarios, for the fault partially intersecting the block.

Three different fault inclinations and two different jointing conditions were

considered, as summarized in Table 5.4:

Table 5.4 Modelling scenarios for analysis of the effect of fault inclination

Scenario Joint sets dips, ° Fault dip, ° Figure

F6

90/0

45 5.18(f)

F2 60 5.18(b)

F7 75 5.18(h)

F8

70/20

45 5.18(g)

F4 60 5.18(c)

F9 75 5.18(i)

Figs. 5.20, 5.30, 5.31 illustrate surface subsidence development at 35, 50 and

60% ore extraction, and, Figs. 5.24(b) and 5.34(a,b) show resultant subsidence

deformations at 100% ore extraction for models F2, F6 and F7, assuming

vertical/horizontal joints. Figs. 5.22, 5.32 and 5.33 present surface subsidence

development at 35, 50 and 60% ore extraction and Figs. 5.23(d) and 5.34(c,d)

show the resultant subsidence deformation at 100% ore extraction for models

F4, F8 and F9, assuming steeply/gently dipping joints. Comparing subsidence

deformation development for varying fault inclinations and varying joint set

orientations it should be noted that, for all assumed inclinations, faults affect the

development of subsidence deformation. Irrespective of jointing orientation

caving induced failure is controlled predominantly by the plane of weakness

provided by the fault. Continuous ore extraction leads to full mobilization of the

entire hanging wall and its disintegration into segments. The mode of hanging

wall segmentation appears to be controlled by joint orientation. Failure of the

hanging wall leads to formation of a crater wall along the footwall of the exposed

fault, which is particularly pronounced for the 75° and 60° faults. For the 75° fault

models (F7, F9, Fig. 5.34(b,d)) exposure of a steep footwall by the caving causes

its partial failure, the magnitude of this failure is strongly controlled by the jointing.

128

35% ore extraction

50% ore extraction

60% ore extraction




50m

90°

0°

129

35% ore extraction

50% ore extraction

60% ore extraction




50m

90°

0°

130

35% ore extraction

50% ore extraction

60% ore extraction




70°

20°

50m

131

35% ore extraction

50% ore extraction

60% ore extraction




70°

20°

50m

132

0-100 -50-150-200-250 10050 150 200 250 300-300

(a)

F6

(b)

F7

(c)

F8

(d)

F9

Fig. 5.34 Subsidence at 100% ore extraction for F6, F7, F8 and F9 models

90°

0°

70°

20°

fault location prior to caving

70°

20°

46°

71°

46°

59°


vertical

horizontal

Legend:


46°

75°

75°

66°

67°

90°

0°

MRV = 40798m3

AI = 0.61

MRV = 29594m3

AI = 0.95

MRV = 43319m3

AI = 0.70

MRV = 33922m3

AI = 0.88

133

Vertical/horizontal jointing contributes to formation of a nearly vertical wall,

whereas inclined jointing favours kinematic instability of major near surface rock

mass blocks. For the 60° faults (F2, F4, Fig. 5.24(b,d)), the moderately inclined

footwall was less exposed and the passive support provided by the muck pile

prevented development of major internal instability. Here it should be noted that

reduction of this support will likely trigger further footwall damage, particularly for

the case with inclined joints. For the 45° faults (F6, F8, Fig. 5.34(a,c)), the

footwall sustained only minor damage. It appears that for the simulated jointing

conditions development of major instability in a 45° footwall slope even with

continuous ore extraction is highly unlikely.

Inclination of the fault significantly alters the extent of the caving influence. For

the 45° and 60° faults, irrespective of the assumed joint set conditions, the extent

of major surface deformation toward the fault was determined by the fault

inclination, so that the angular limits of major ( 10cm) surface displacements are

equal or nearly equal to the fault inclination. For the 75° faults the extent of

major surface deformations is a function of stability of the exposed footwall. For

the model with vertical/horizontal joints the limiting angle is 75 , whereas for the

model with inclined joints it is 59 .

Comparison of the extent of major surface displacements for the models with

vertical/horizontal joints without a fault (Base Case) and with fault dips of 75

(F6), 60 (F2) and 45 (F7) is presented in Fig. 5.35. This figure shows that

faults with inclinations of 60 and 45 extended the total zones of major

displacement by about 20 and 60%, respectively. In the direction towards the

fault, for 60 and 45 dipping faults, the zone of influence was increased by 40

and 120%, respectively, i.e. a decrease in fault inclination by 15 extended the

zone of major surface displacements by 80%. The fault with 75 inclination had

only a minor influence on the observed extent of major surface displacements.

Comparison of the extent of major surface displacements for the models with

inclined joints without a fault (J2) and with a fault of 75 (F9), 60 (F4) and 45

(F8) inclination is given in Fig. 5.36. As follows from this figure for faults with 60

134

and 75 inclination the extent of the zone of major surface displacement towards

the fault was reduced by as much as 50%. The surface outcrop location of the

45 fault coincided approximately with the extent of major displacements for the

model without a fault (see Figs. 5.6(c), 5.34(d)), hence no major influence was

observed. Interestingly models with 45 and 75 dipping faults exhibit increased

zones of influence in an eastward direction from the block centre vertical axis.

207 204

255

331

100%

102% 125% 161%

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

To

tal exte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts

no

rmalized

b

y B

ase C

ase, %

To

tal e

xte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts,

m

BC F7 F2 F6

218 222

258

350

100%

102%

118% 161%

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

To

tal exte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts

no

rmalized

b

y B

ase C

ase, %

To

tal e

xte

nt o

f 10cm

ho

riz.

su

rface d

isp

lacem

en

ts,

m

BC F7 F2 F6

-112

95

-102

102

-160

95

-245

8691%

219%

100%

143%

107%

91%

100%

100%

-300 -200 -100 0 100 200 300

-250 -200 -150 -100 -50 0 50 100 150 200 250



BC

F7

F2

F6

BC

F7

F2

F6

-118

100

-102

120

-160

98

-245

105105%

208%

98%

136%

120%

86%

100%

100%

-300 -200 -100 0 100 200 300

-250 -200 -150 -100 -50 0 50 100 150 200 250



BC

F7

F2

F6

BC

F7

F2

F6

Fig. 5.35 Subsidence characterization for BC, F2, F6 and F7 models Total extent of major (≥10cm) vertical (a) and horizontal (b) surface displacements in m and in % of Base Case value; extent of 10cm surface vertical (c) and horizontal (d) displacements in relation to centre axis of the block, in m

Far-field displacements for models with vertical/horizontal and inclined joints are

presented in Figs. 5.37 and 5.38 respectively. It can be inferred from these

figures that, in the direction towards the fault, the extent of the far-field

displacements is a function of fault inclination. A shallower fault inclination

resulted in a larger area mobilized by the caving. Conversely, steeper faults limit

such an area. Within the failing hanging wall higher deformation magnitudes

were observed for models with vertical/horizontal joints.

(a) (b)

(c) (d)

135

268254

269

100%

95%

100% 1

40%

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

To

tal e

xte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts

no

rmalized

by J

2, %

To

tal e

xte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts,

m

375

J2 F9 F4 F8

308 305

268

100%

99%

87% 125%

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

To

tal e

xte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts

no

rmalized

by J

2, %

To

tal e

xte

nt o

f 10cm

ho

riz.

su

rface d

isp

lacem

en

ts,

m

J2 F9 F4 F8

384

-161

107

-126

128

-161

108

-245

130151%

100%

126%

66%

149%

51%

100%

100%

-350 -250 -150 -50 50 150 250 350

-250 -200 -150 -100 -50 0 50 100 150 200 250



J2

F9

F4

F8

J2

F9

F4

F8

-245

105

-169

136

-160

108

-245

139132%

100%

103%

65%

130%

69%

100%

100%

-300 -200 -100 0 100 200 300

-250 -200 -150 -100 -50 0 50 100 150 200 250



J2

F9

F4

F8

J2

F9

F4

F8

Fig. 5.36 Subsidence characterization for J2, F4, F8 and F9 models Total extent of major (≥10cm) vertical (a) and horizontal (b) surface displacements in m and in % of J2 value; extent of 10cm surface vertical (c) and horizontal (d) displacements in relation to centre axis of the block, in m

F6

F6

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

-300 -250 -200 -150 150 200 250 300

Vert

ical d

isp

lacem

en

ts,

m


-2

F2

-0.8-0.8

BC BC

F7 F7

F2

F2

F6 F6

F6

0

0.05

0.1

0.15

0.2

0.25

0.3

-300 -250 -200 -150 150 200 250 300

Ho

rizo

nta

l d

isp

lacem

en

ts, m


1.20.8 0.8

Fig. 5.37 Total vertical (a) and horizontal (b) surface displacements at the end of ore extraction at different distances from block centre for Base Case, F2, F6 and F7 models

(a) (b)

(c) (d)

(a)

(b)

136

J2

J2

F9 F4

F8

F8

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

-300 -250 -200 -150 150 200 250 300

Vert

ical d

isp

lacem

en

ts,

m


-0.4

J2

J2

J2

J2F9

F9

F9

F4

F4

F4F8

F8

F8

F8

0

0.05

0.1

0.15

0.2

0.25

0.3

-300 -250 -200 -150 150 200 250 300

Ho

rizo

nta

l d

isp

lacem

en

ts, m


0.450.8

Fig. 5.38 Total vertical (a) and horizontal (b) surface displacements at the end of ore extraction at different distances from block centre for J2, F4, F8 and F9 models

Depending on the fault inclination the amount of differential displacement at the

surface outcrop of the fault will vary, higher displacements being observed for

models with steeper faults (see Fig. 5.39).

Fig. 5.39 Differential XY displacements for surface points on the fault hanging and foot walls for F2, F6 and F7 models

footwall

hanging

wall

differential

XY displacement

-4.31m

-2.37m

-0.02m

-5

-4

-3

-2

-1

0

0 10 20 30 40 50 60 70 80 90 100

Dif

fere

nti

al

XY

d

isp

lac

em

en

ts, m

Ore extraction, %

F1

F2

F3hangingwall desintegrated

-1.16m

-2.37m

-5

-4

-3

-2

-1

0

0 10 20 30 40 50 60 70 80 90 100

Dif

fere

nti

al

XY

d

isp

lac

em

en

ts, m

Ore extraction, %

F7

F2

F6

hangingwall desintegrated

-1.36m

(a)

(b)

90°

0°

70°

20°

137

The following can be concluded based on the ELFEN modelling results, with respect

to the effect of fault inclination on block caving induced surface subsidence:

1. Unequivocally, the inclination of the fault partially intersecting the

caving area controls the extent of surface subsidence deformations.

Low dipping faults will extend and steeply dipping faults will decrease

the area of surface subsidence.

2. For faults daylighting into the cave, failure of the hanging wall is likely

inevitable. For the assumed hard rock mass conditions in the current

modelling, the stability of the exposed footwall is dependent on its slope,

the amount of passive support provided by the muck pile and the

orientation and persistence of jointing within the footwall. The presence

of well defined steeply/gently dipping joint set approaching

perpendicular orientation with relation to the fault will increase the

kinematic potential for failure of major near surface footwall segments.

In such circumstances a model combining the fault/jointing system is

extremely important.

Both conclusions are in agreement with observations by Abel & Lee (1980) and

Stacey & Swart (2001).

5.5 Influence of Rock Mass Strength and Deformability Characteristics

The effects of rock mass strength and deformability characteristics were

evaluated based on three modelling scenarios, using model J2 as a basis:

I. RM1 (70°/20°; rock mass tensile strength reduced by 40%, from 1 MPa to

0.6MPa);

II. RM2 (70°/20°; rock mass tensile strength increased by 40%, from 1 MPa to

1.4MPa);

III. RM3 (70°/20°; rock mass deformation modulus increased by 30%, from

18GPa to 23GPa).

138

The mechanism of surface subsidence development for models RM1 and RM3 was

very similar to model J2, shown in Fig. 5.3(a), exhibiting gradual formation of the

subsidence crater. For model RM2, however, an increase in the tensile strength of

the rock mass reduced rock mass cavability, leading to cave propagation arrest at

about block height. Continuous ore extraction resulted in formation of a significant

expansion void, reaching a height of more than 50m, as illustrated in Fig. 5.40(a). At

55% ore extraction large portions of the crown pillar began to detach and by 57%

ore extraction the crown pillar had fully disintegrated and collapsed into the

expansion void, Fig. 5.40(c). The subsidence crater was formed as a result of a

single failure event rather than gradual cave propagation. Similar behaviour was

observed during a caving physical model test by Kvapil (2004), Fig. 4.6(c,d). It

should be noted that sudden crown pillar collapse can cause a major airblast leading

to dramatic consequences such as that which occurred at Northparkes block cave

mine (Hebblewhite, 2003).

Fig. 5.41 presents subsidence profiles at 100% ore extraction for models RM1,

RM2 and RM3. Comparing Figs. 5.42(a,b) and 5.6(c) it can be noted that a

decrease in rock mass tensile strength by 40% increased subsidence deformation

so that the minimum angle delineating major ( 10cm) surface displacements was

decreased by 3 . An increase in rock mass tensile strength by 40% led to higher

rock mass resistance to mobilization, consequently increasing the minimum

delineating angle by 7 . An increase in the rock mass deformation modulus by

30% had practically no influence on the resultant subsidence deformations.

Comparing the extent of major ( 10cm) surface subsidence displacements for

models J2, RM1, RM2 and RM3, Fig. 5.42, it can be noted that depending on the

decrease or increase in rock mass tensile strength the maximum extent of

subsidence displacement in the westward direction is increased by 7% or

decreased by 16%, respectively. Changes in rock mass deformability did not

result in any noticeable difference in the extent of major surface displacements.

139

(a) 35%

(b) 50%

(c) 55% (d) 56%

(e) 57% (f) 60%



Fig. 5.40 Stages of subsidence crater formation at different percentages of ore block extraction for model RM2 (a) - (b) cave propagation arrest and formation of expansion void; (b) - (e) crown pillar collapse and formation of subsidence crater

50m

140

0-100 -50-150-200-250 10050 150 200 250 300-300

(a)

RM1

(b)

RM2

(c)

RM3

Fig. 5.41 Subsidence at 100% ore extraction for models RM1, RM2 and RM3

Comparison of the far-field surface displacements for the same models, given in

Fig. 5.43, showed no significant difference at either the extent of surface

displacements or their magnitude.

ELFEN modelling demonstrated that for the assumed variations in rock mass

tensile strength and deformability, the effect on the resultant subsidence

deformations was limited. Modelling demonstrated however that an increase in

rock mass tensile strength may have a profound influence on the manner of cave

propagation and subsidence crater formation mechanism.

70°

20°

50°

69°

53°


horizontal

Legend:


50°

69°

60°

73°

70°

20°

70°

20°

rock mass tensile str. (-)40%

rock mass tensile str. (+)40%

rock mass deformability (+)30%

MRV = 37512m3

AI = 0.72

MRV = 35885m3

AI = 0.87

MRV = 36479m3

AI = 0.73

141

268 260283 282

100%

97%

106%

105%

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

To

tal e

xte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts

no

rmalized

by J

2, %

To

tal e

xte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts,

m

J2 RM1 RM2 RM3

308343

297314

100%

111%

96%

102%

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

To

tal exte

nt o

f 10cm

ho

riz.

su

rface d

isp

lacem

en

ts

no

rmalized

b

y J

2, %

To

tal exte

nt o

f 10cm

ho

rz.

hsu

rface d

isp

lacem

en

ts,

m

J2 RM1 RM2 RM3

-161

107

-140

120

-163

120

-169

113106%

105%

112%

101%

112%

87%

100%

100%

-300 -200 -100 0 100 200 300

-250 -200 -150 -100 -50 0 50 100 150 200 250



J2

RM1

RM2

RM3

J2

RM1

RM2

RM3

-201

107

-215

128

-169

128

-201

113106%

100%

120%

84%

120%

107%

100%

100%

-300 -250 -200 -150 -100 -50 0 50 100 150 200 250 300

-250 -200 -150 -100 -50 0 50 100 150 200 250



J2

RM1

RM2

RM3

J2

RM1

RM2

RM3

Fig. 5.42 Subsidence characterization for models J2, RM1, RM2 and RM3 Total extent of major (≥10cm) vertical (a) and horizontal (b) surface displacements in m and in % of Base Case value; extent of 10cm surface vertical (c) and horizontal (d) displacements in relation to centre axis of the block, in m

J2

J2

RM

1

RM

1R

M2

RM

3

RM

3

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

-300 -250 -200 -150 150 200 250 300

Vert

ical d

isp

lacem

en

ts,

m


-0.38 -0.37

J2

J2

J2

J2

RM

1

RM

1

RM

1

RM

1

RM

2

RM

2

RM

2

RM

2

RM

3

RM

3

RM

3

RM

3

0

0.05

0.1

0.15

0.2

0.25

0.3

-300 -250 -200 -150 150 200 250 300

Ho

rizo

nta

l d

isp

lacem

en

ts, m


0.67 0.440.8

Fig. 5.43 Total vertical (a) and horizontal (b) surface displacements at the end of ore extraction at different distances from block centre for models J2, RM1, RM2 and RM3

(a) (b)

(c) (d)

(a)

(b)

142

5.6 Influence of Stress Environment

The influence of the in-situ stress environment on caving induced surface

subsidence development was evaluated by analyzing the effect of change in the

ratio between horizontal and vertical stresses, K. Default modelling conditions

assume hydrostatic stress, K=1, i.e. horizontal and vertical stress are equal. Two

additional assumptions were considered, K=0.5 (200% higher vertical stress) and

K=2 (200% higher horizontal stress). To appreciate the variation in response in

different geological settings, simulations with vertical/horizontal and

steeply/gently dipping joints sets, based on Base Case and J2 models,

respectively, were considered, as summarized in Table 5.5:

Table 5.5 Modelling scenarios for analysis of the effect of stress environment

Scenario Joint sets dips, ° Stress ratio, K

S1 90/0

0.5

S2 2

S3 70/20

0.5

S4 2

Variation in the assumed K ratio did not have any noticeable affect on

subsidence crater formation mechanism and therefore is not shown here.

Resultant surface subsidence deformations at 100% ore extraction for the S1 to

S4 models are given in Fig. 5.44. Comparing models with vertical/horizontal joint

sets, shown in Figs. 5.6(a) and 5.44(a,b), no significant difference in subsidence

deformations can be observed. The same conclusion can be reached for models

with inclined joints, see Figs. 5.6(c) and 5.44(c,d). In terms of the limiting angles

delineating major ( 10cm) subsidence displacements, generally higher angles

are observed for the lower K, and lower angles for the higher K ratio.

Figs. 5.45 and 5.46 compare the extent of major surface subsidence

displacements for models with vertical/horizontal (BC, S1 and S2) and

steeply/gently dipping (J2, S3 and S4) joint sets, respectively. It is interesting to

note that influence of lower K ratio on the extent of major surface subsidence

displacements is more marked than for a higher K ratio. For the models with

vertical/horizontal joints the total extent of major displacements was reduced by a

143

maximum of 6% for K=0.5 and increased by only 2% for K=2. Similar changes

for simulations with inclined joints were 16% and 5%, for K=0.5 and 2

respectively.

If for major subsidence deformation the effect of varying K is relatively subtle, the

influence of the K ratio on far-field displacements is far more pronounced, as

shown in Figs. 5.47 and 5.48. In comparison with models with the lower K ratio,

simulations with K=2 (S2 and S4) exhibited significantly larger magnitudes (up to

5 times) of horizontal far-field displacements. For the model with

vertical/horizontal joint sets (S2), in both the westward and eastward direction

from the block centre vertical axis, a nearly equal increase in displacements is

observed. In contrast for the model with inclined joint sets (S4), higher

displacements (up to 3 times at 250m from caving boundary) in the westward

direction are observed.

Overall, ELFEN modelling to investigate the influence of in-situ stress

environment on block caving induced subsidence, provides the following

conclusions:

1. In general, lower horizontal in-situ stress results in a smaller area affected

by subsidence deformations.

2. Simulations with different joint patterns did not exhibit major differences in

the effect of varying K ratio on surface subsidence development and the

extent of major subsidence displacements.

3. Higher horizontal stresses (K=2), lead to elevated magnitudes of far-field

horizontal surface displacements. A combination of higher horizontal

stresses and inclined joints promoted higher displacement magnitudes in

the dip direction of a steeply dipping set.

144

0-100 -50-150-200-250 10050 150 200 250 300-300

(a)

S1

(b)

S2

(c)

S3

(d)

S4

Fig. 5.44 Subsidence at 100% ore extraction for models S1, S2, S3 and S4

70°

20°

73°

75°

55°


horizontal

Legend:


73°

78°

71°

70°

K=0.5

K=2

K=0.5

K=2 53°

74°

70°

20°

90°

0°

90°

0°

MRV = 28580m3

AI = 0.94

MRV = 31487m3

AI = 0.95

MRV = 33165m3

AI = 0.74

MRV = 35654m3

AI = 0.76

145

204 207 212

99%

100%

102%

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

To

tal e

xte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts

no

rmalized

by B

ase C

ase, %

To

tal exte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts,

m

S1 BC S2

204218 222

94%

100%

102%

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

To

tal e

xte

nt o

f 10cm

ho

riz.

su

rface d

isp

lacem

en

ts

no

rmalized

by B

ase C

ase, %

To

tal e

xte

nt o

f 10cm

h

ori

z.

su

rface d

isp

lacem

en

ts,

m

S1 BC S2

-112

92

-112

95

-110

102107%

98%

100%

100%

97%

100%

-300 -200 -100 0 100 200 300

-250 -200 -150 -100 -50 0 50 100 150 200 250



S1

BC

S2

S1

BC

S2

-112

92

-118

100

-115

107107%

97%

100%

100%

92%

95%

-300 -200 -100 0 100 200 300

-250 -200 -150 -100 -50 0 50 100 150 200 250



S1

BC

S2

S1

BC

S2

Fig. 5.45 Subsidence characterization for models Base Case, S1 and S2 Total extent of major (≥10cm) vertical (a) and horizontal (b) surface displacements in m and in % of Base Case value; extent of 10cm surface vertical (c) and horizontal (d) displacements in relation to centre axis of the block, in m

226

268 279

84%

100%

104%

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

To

tal e

xte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts

no

rmalized

b

y J

2, %

To

tal e

xte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts,

m

S3 J2 S4

296 308324

96%

100%

105%

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

To

tal exte

nt o

f 10cm

ho

riz.

su

rface d

isp

lacem

en

ts

no

rmalized

b

y J

2, %

To

tal exte

nt o

f 10cm

ho

riz.

su

rface d

isp

lacem

en

ts,

m

S3 J2 S4

-118

108

-161

107

-156

123115%

97%

100%

100%

101%

73%

-300 -200 -100 0 100 200 300

-250 -200 -150 -100 -50 0 50 100 150 200 250



S3

J2

S4

S3

J2

S4

-189

107

-201

107

-201

123115%

100%

100%

100%

100%

94%

-300 -200 -100 0 100 200 300

-250 -200 -150 -100 -50 0 50 100 150 200 250



S3

J2

S4

S3

J2

S4

Fig. 5.46 Subsidence characterization for models J2, S3 and S4 Total extent of major (≥10cm) vertical (a) and horizontal (b) surface displacements in m and in % of J2 value; extent of 10cm surface vertical (c) and horizontal (d) displacements in relation to centre axis of the block, in m

(a) (b)

(c) (d)

(a) (b)

(c) (d)

146

S1

BC BC

S2 S

2 S2 S2

S2

S2

S2

S2

0

0.05

0.1

0.15

0.2

0.25

0.3

-300 -250 -200 -150 150 200 250 300

Ho

rizo

nta

l dis

pla

cem

en

ts, m


Fig. 5.47 Total horizontal surface displacements at the end of ore extraction at different distances from block centre for models Base Case, S1 and S2

S3

J2

J2

S4

S4

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

-300 -250 -200 -150 150 200 250 300

Vert

ical d

isp

lacem

en

ts,

m


0.9 3.8

S3

S3

S3

J2

J2

J2

J2S

4 S4 S

4

S4

S4

S4

S4

S4

0

0.05

0.1

0.15

0.2

0.25

0.3

-300 -250 -200 -150 150 200 250 300

Ho

rizo

nta

l dis

pla

cem

en

ts, m


0.8 0.7

Fig. 5.48 Total vertical (a) and horizontal (b) surface displacements at the end of ore extraction at different distances from the block centre for models J2, S3 and S4

(a)

(b)

147

5.7 Influence of Varying Lithological Domains

Natural rock masses are highly heterogeneous and consist of domains of varying

competency and discontinuity networks. The default modelling conditions

assumed identical properties throughout the simulated rock mass and did not

account for possible variation in discontinuity orientation between the ore and

surrounding host rock. This section investigates the influence of varying rock

mass strength and jointing pattern, between the ore body and the surrounding

host rock, on block caving induced surface subsidence.

5.7.1 Effect of Varying Strength between Ore and Host Rock

The effect of variation in rock mass strength was analyzed by assuming a stronger

host rock and increasing its tensile strength by 40% (from 1MPa to 1.4MPa). Rock

mass conditions with and without a caprock, as illustrated in Fig. 5.49, were

considered.

0-100 -50-150-200-250 10050 150 200 250 300-300

(a) GD1

(c) GD3

(b) GD2

(d) GD4

Fig. 5.49 Assumed geometries for models GD1 to GD4

90°

0°

ore

stronger host rock

ore stronger host rock

stronger host rock

90°

0°

extracted ore block

70°

20°

70°

20°

148

For each assumed rock mass strength condition assumption two modelling

scenarios with varying joint orientation (as in Base Case and J2 models) were

considered, as summarized in Table 5.6:

Table 5.6 Modelling scenarios for analysis of the effect of varying strength between ore and host rock

Scenario Joint sets dips, ° Caprock Figure

GD1 90/0

+ 5.49(a)

GD2 - 5.49(b)

GD3 70/20

+ 5.49(c)

GD4 - 5.49(d)

Figs. 5.50 and 5.51 illustrate subsidence crater development with continuous ore

extraction for the above models. Comparing simulations with vertical/horizontal

joints (GD1, GD2) it can be seen that the presence of a stronger caprock delayed

formation of a subsidence crater. As shown in Fig. 5.50(a), cave propagation

arrested just above the boundary of the ore block. With continuous ore extraction

an expansion void was formed, reaching a maximum height of about 30m at 45%

ore extraction. At this point the crown pillar began to fracture and rapidly

disintegrate, in a similar fashion as for RM2 model (Fig. 5.40). In contrast, it is

evident from Fig. 5.50(b) that for a model without a stronger caprock the

subsidence crater developed gradually. Comparing this model with the Base Case,

shown in Fig. 5.2(a), it can be inferred that the stronger host rock limited the extent

of fracturing damage outside the ore body boundaries and resulted in an initial

subsidence crater with nearly vertical walls. It is worth noting that rapid crown pillar

collapse for the model with a caprock led to increased fracturing damage in the

near surface rock mass. Comparing subsidence crater development for

simulations with inclined joints (GD3, GD4) and the reference model J2, Fig. 5.3(a),

it appears that the stronger host rock significantly limited the amount of rock mass

mobilized by the failure; cave propagation was largely vertical, although some

preferential fracturing along the steeply dipping set was apparent. Contrasting

models GD3 (Fig. 5.51(a)) and GD4 (Fig. 5.51(b)) it is apparent that the presence

of a stronger caprock reduced the fracturing damage in the rock mass westward

149

from the block centre vertical axis and prevented development of large scale rock

mass failure.

(a) GD1 (b) GD2

35% 35%

50% 50%

60% 60%



Fig. 5.50 Subsidence crater formation for models (a) GD1 with a caprock and (b) GD2 without a caprock

50m

150

(a) GD3

(b) GD4

35% 35%

50% 50%

60% 60%



Fig. 5.51 Subsidence crater formation for models (a) GD3 with a caprock and (b) GD4 without a caprock

50m

151

Resultant surface subsidence at 100% ore extraction for all lithological domain

models is given in Fig. 5.52.

0-100 -50-150-200-250 10050 150 200 250 300-300

(a)

GD1

caprock

(b)

GD2

(c)

GD3

caprock

(c)

GD4

Fig. 5.52 Subsidence at 100% ore extraction for models (a) GD1, (b) GD2, (c) GD3 and (d) GD4

70°

20°

74°

76°

75°


horizontal

Legend:


73°

77°

73°

69°

63° 74°

70°

20°

90°

0°

90°

0°

MRV = 27888m3

AI = 0.96

MRV = 27095m3

AI = 0.96

MRV = 28661m3

AI = 0.92

MRV = 32862m3

AI = 0.85

152

For the simulations with vertical/horizontal joints, surface subsidence

deformations are nearly symmetrical with respect to the block centre vertical axis.

In contrast to the Base Case model, see Fig. 5.6(a), the stronger host rock

resulted in slightly steeper angles delineating major ( 10cm) surface

deformations (to a maximum of 3°). Assumption of a caprock led to only a minor

1° increase in delineating angles. For the simulations with inclined joints, the

influence of a higher host rock strength was quite dramatic. Models with a

caprock showed higher asymmetry in the eastward direction. The delineating

angle in the westward direction was 75°, which is 24° steeper than for model J2

(Fig. 5.6(c)). The corresponding angle for the model without a caprock was 63°,

or 12° steeper than for J2 model.

As shown in Fig. 5.53, for models with vertical/horizontal joints the presence of a

stronger host rock reduced the total extent of major surface displacements by a

negligible amount. Compared to the Base Case model a maximum reduction of

6% was observed for the model with caprock (GD1) and only a 2% reduction was

exhibited by the model without a caprock (GD2). According to Fig. 5.54, for

models with inclined joints, the maximum reduction in the extent of major surface

displacements of 35% was observed for the case with a caprock (GD3), whereas

for the case without a caprock (GD4), the reduction was 15%. Notably, for both

models the extent of surface subsidence was reduced primarily in the direction of

the joint controlled subsidence asymmetry, suggesting a decreasing rock mass

susceptibility to toppling failure with increased rock mass tensile strength. An

increase in host rock mass tensile strength by 40% caused a reduction in the

extent of major surface displacements in the westward direction by a maximum

of 49% for the model with and 24% for the model without a caprock.

Far-field displacements for GD1 and GD2 did not differ from the Base Case

values and therefore are not shown here. Far-field displacements for GD3 and

GD4 models are given in Fig. 5.55, it can be seen that the stronger host rock

moderately decreased the displacement magnitudes.

153

207 195 204

100%

94%

99%

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

To

tal exte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts

no

rmalized

b

y B

ase C

ase, %

To

tal e

xte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts,

m

BC GD1 GD2

218 207 214

100%

95%

98%

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

To

tal e

xte

nt o

f 10cm

ho

riz.

su

rface d

isp

lacem

en

ts

no

rmalized

by B

ase C

ase, %

To

tal e

xte

nt o

f 10cm

ho

riz.

su

rface d

isp

lacem

en

ts,

m

BC GD1 GD2

-112

95

-109

86

-110

9499%

98%

91%

97%

100%

100%

-300 -200 -100 0 100 200 300

-250 -200 -150 -100 -50 0 50 100 150 200 250



BC

GD1

GD2

BC

GD1

GD2

-118

100

-109

98

-110

104104%

93%

98%

92%

100%

100%

-300 -200 -100 0 100 200 300

-250 -200 -150 -100 -50 0 50 100 150 200 250



BC

GD1

GD2

BC

GD1

GD2

Fig. 5.53 Subsidence characterization for models Base Case, GD1 and GD2 Total extent of major (≥10cm) vertical (a) and horizontal (b) surface displacements in m and in % of Base Case value; extent of 10cm surface vertical (c) and horizontal (d) displacements in relation to centre axis of the block, in m

268

193

260

100%

72% 97%

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

To

tal exte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts

no

rmalized

b

y J

2, %

To

tal exte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts,

m

J2 GD3 GD4

308

200

261

100%

65%

85%

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

To

tal e

xte

nt o

f 10cm

ho

riz.

su

rface d

isp

lacem

en

ts

no

rmalized

by J

2, %

To

tal e

xte

nt o

f 10cm

ho

riz.

su

rface d

isp

lacem

en

ts,

m

J2 GD3 GD4

-161

107

-100

93

-152

108101%

94%

87%

62%

100%

100%

-300 -200 -100 0 100 200 300

-250 -200 -150 -100 -50 0 50 100 150 200 250



J2

GD3

GD4

J2

GD3

GD4

-201

107

-102

98

-152

109102%

76%

92%

51%

100%

100%

-300 -200 -100 0 100 200 300

-250 -200 -150 -100 -50 0 50 100 150 200 250



J2

GD3

GD4

J2

GD3

GD4

Fig. 5.54 Subsidence characterization for models J2, GD3 and GD4 Total extent of major (≥10cm) vertical (a) and horizontal (b) surface displacements in m and in % of J2 value; extent of 10cm surface vertical (c) and horizontal (d) displacements in relation to centre axis of the block, in m

(a) (b)

(c) (d)

(a) (b)

(c) (d)

154

J2

J2

GD

4

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

-300 -250 -200 -150 150 200 250 300

Vert

ical d

isp

lacem

en

ts,

m


0.4

J2

J2

J2

J2

GD

3

GD

3

GD

3

GD

3

GD

4

GD

4 GD

4

GD

4

0

0.05

0.1

0.15

0.2

0.25

0.3

-300 -250 -200 -150 150 200 250 300

Ho

rizo

nta

l d

isp

lacem

en

ts, m


0.8

Fig. 5.55 Total vertical (a) and horizontal (b) surface displacements at the end of ore extraction at different distances from block centre for models J2, GD3 and GD4

Overall, with regards to the influence of varying rock mass strength on caving

induced surface subsidence, the ELFEN results indicate the following:

1. An increase in the strength of the rock mass surrounding the excavated

block reduces the subsidence deformation. The magnitude of reduction in

subsidence deformations is highly dependent on assumed rock mass

jointing conditions. For the assumed increase in host rock tensile strength

simulations with vertical/horizontal joints, results indicated a generally

minor influence on the resultant surface subsidence. Simulations with

inclined joints showed a marked decrease in subsidence deformation

primarily in the dip direction of the steeply inclined joint set.

2. The presence of a stronger caprock may cause a temporary arrest in the

cave propagation followed by a rapid crown pillar collapse.

5.7.2 Effect of Varying Joint Orientation within the Ore and Host Rock

The influence of varying jointing was investigated by assuming that the ore body

extends to the surface and has a different joint orientation to the surrounding host

(a)

(b)

155

rock. Here it should be recognized that in natural rock masses the contact

between varying discontinuities patterns is not well defined. Typically there is a

transition zone, where patterns overlap. The extent of such a transition zone,

depends on a variety of factors primarily related to tectonic history. For the

preliminary conceptual analysis an idealized condition with minor discontinuity set

overlap was adopted, as shown in Fig. 5.56.

(a) GD5

host rock

ore

(b) GD6

host rock

ore

Fig. 5.56 Assumed modelling geometries for models (a) GD5 and (b) GD6

Two modelling scenarios were considered, as summarized in Table 5.7:

Table 5.7 Modelling scenarios for analysis of the effect of varying joint orientation within the ore and host rock

Scenario Host rock joint sets dips, °

Ore body joint sets dips, °

Figure

GD5 90/0 70/20 5.56(a)

GD6 70/20 90/0 5.56(b)

Subsidence crater development for the above models is illustrated in Fig. 5.57. It

can be inferred from Fig. 5.57(a) that inclined joints within the ore initially

promoted skewed cave propagation in an eastward direction, terminating against

the host rock with vertical/horizontal joints and then became nearly vertical. As a

70°

20°

90°

0°

70°

20°

90°

0°

156

result of inclined cave propagation, a major rock mass segment overhanging the

caved block was formed and eventually toppled into the cave. As follows from

Fig. 5.57(b), for the ore with vertical/horizontal joints cave propagation was

generally vertical, although inclined joints in the host rock caused rock mass

mobilization and fracturing damage that resembles the response of model J2

(Fig. 5.3(a)).

The resultant surface subsidence deformation and subsidence displacement

characterization for models GD5 and GD6 are presented in Figs. 5.58 and 5.59,

respectively. Comparing subsidence deformations for model GD5 (Fig. 5.58(a))

and the Base Case (Fig. 5.6(a)) it can be noted that inclined orientation of the

joints within the ore surrounded by a host rock with vertical/horizontal joints had

practically no influence on caving induced subsidence, the angles delineating

major ( 10cm) surface displacements being identical. As apparent from Fig.

5.59, the total extent of major subsidence displacement for model GD5 was

changed by a maximum of 3%. Comparison of models GD6 (Fig. 5.58(b)) and J2

(Fig. 5.6(c)) shows that the assumption of vertical/horizontal joints for the ore

resulted in a decrease in rock mass fracturing damage and steepened the

delineating angles by up to 5°. According to Fig. 5.59, the total extent of

maximum major surface displacements was reduced by 9%, with larger

reductions in deformations being observed in the eastward direction.

Fig. 5.60 compares far-field surface displacements for the Base case, GD5, J2

and GD6 models. GD5 exhibited a minor increase and GD6 showed a minor

decrease in the far field displacements.

Overall, the ELFEN modelling performed showed that the host rock jointing

pattern has an important influence on caving induced surface subsidence

development.

157

(a) GD5

(b) GD6

35% 35%

50% 50%

60% 60%

Legend: rotational failure; translational failure


Fig. 5.57 Subsidence crater formation for models GD5 and GD6

50m

158

0-100 -50-150-200-250 10050 150 200 250 300-300

(a)

GD5

host rock

90°/0°

ore 70°/20°

(b)

GD6

host rock

70°/20°

ore 90°/0°

Fig. 5.58 Subsidence at 100% ore extraction for models GD5 and GD6

207 203

268

218

100%

98%

100%

81%

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

To

tal e

xte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts

no

rmalized

by B

C/J

2, %

To

tal e

xte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts,

m

BC GD5 J2 GD6

218 212

308279

100%

97%

100%

91%

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

To

tal e

xte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts

no

rmalized

by B

C/J

2,

%

To

tal e

xte

nt o

f 10cm

ho

riz.

su

rface d

isp

lacem

en

ts,

m

BC GD5 J2 GD6

-112

95

-109

94

-161

107

-128

9084%

80%

100%

100%

99%

97%

100%

100%

-300 -200 -100 0 100 200 300

-250 -200 -150 -100 -50 0 50 100 150 200 250

Extent of 10cm surface vertical displacements in relation to block centre, normalized by BC/J2, %


BC

GD5

J2

GD6

BC

GD5

GD6

J2

-118

100

-118

94

-201

107

-189

9084%

94%

100%

100%

94%

100%

100%

100%

-300 -250 -200 -150 -100 -50 0 50 100 150 200 250 300

-250 -200 -150 -100 -50 0 50 100 150 200 250

Extent of 10cm surface horizontal displacements in relation to block centre, normalized by BC/J2, %


BC

GD5

J2

GD6

BC

GD5

GD6

J2

Fig. 5.59 Subsidence characterization for models Base Case, J2, GD5 and GD6 Total extent of major (≥10cm) vertical (a) and horizontal (b) surface displacements in m and in % of J2 value; extent of 10cm surface vertical (c) and horizontal (d) displacements in relation to centre axis of the block, in m

71°

79°


vertical

horizontal

Legend:


73°

78°

55°

(a) (b)

(c) (d)

MRV = 28415m3

AI = 0.91

MRV = 33531m3

AI = 0.70

159

J2

GD

6

GD

6

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

-300 -250 -200 -150 150 200 250 300

Vert

ical d

isp

lacem

en

ts,

m


-0.38

J2

B

C

BC

GD

5

GD

5

J2

J2

J2

J2GD

6 GD

6

GD

6

GD

6

0

0.05

0.1

0.15

0.2

0.25

0.3

-300 -250 -200 -150 150 200 250 300

Ho

rizo

nta

l dis

pla

cem

en

ts, m


-0.8

Fig. 5.60 Total vertical (a) and horizontal (b) surface displacements at the end of ore extraction at different distances from block centre for models Base Case, J2, GD5 and GD6

(a)

(b)

160

5.8 Influence of Block Depth and Excavation Volume

This section investigates the influence of depth of the extracted ore block and the

volume of the extracted ore on surface subsidence development. The default

model setup assumed a 100m×100m block located at 200m depth, and the

simulations were run up to 100% block volume extraction. Here two scenarios

are considered with the block located at 300m depth, and jointing corresponding

to Base Case and J2 models was assumed:

I. BD1 (90°/0°; 300m block depth)

II. BD2 (70°/20°; 300m block depth)

These scenarios were run up to 100 and 150% block volume extraction. In addition,

scenarios Base Case and J2 were run up to 150% block volume extraction.

Fig. 5.61 illustrates formation of a surface subsidence crater with continuous ore

extraction for models BD1 and BD2. For both models at earlier stages of ore

extraction (up to 30%), caving induced fracturing damage closely resembles an

ellipsoid, with a more slender shape observed for the model with vertical/horizontal

joints (BD1). This caving shape corresponds to the limit ellipsoid defined by

Janelid & Kvapil (1966) based on material draw studies. According to these

authors, the limit ellipsoid contains the zone of broken material that has moved and

expanded under gravity to fill the volume created by draw. Similar ellipsoids can

be delineated for the corresponding Base Case (Fig. 5.2(a)) and J2 (Fig. 5.3(a))

models with a shallower located block. Bétournay (2002) stated that complete

failure of the crown pillar should be anticipated if the draw ellipsoid intersects the

surface, this was actually the case for the studied models. As follows from Fig.

5.61, for the simulation with vertical/horizontal joints the long axis of the ellipsoid

was vertical, with rotation of the pattern by 20° skewing this axis by 7°. Continuous

ore extraction led to a limited, largely symmetrical mobilization of the near surface

rock mass for model BD1, whereas for model BD2 extended and asymmetrical

rock mass mobilization was observed. It appears that for model BD2 major rock

mass mobilization was initiated between 30-40% ore extraction when full

disintegration of the crown pillar occurred.

161

Fig. 5.61 Subsidence crater formation for models BD1 and BD2

(a) BD1 (b) BD2

30%

ore

extr

actio

n

40%

ore

extr

actio

n

50%

ore

extr

actio

n

60%

ore

extr

actio

n

70%

ore

extr

actio

n

50m

70°

20°

50m

90°

0°

7°

162

Fig. 5.62 shows the resultant surface subsidence for model BD1 at 100 and

150% ore extraction. The increase in surface subsidence damage due to an

additional 50% ore extraction was rather minor, the angles delineating major (≥

10cm) subsidence deformations decreasing by 2 to 5 degrees. A comparable

delineating angle can be observed when contrasting subsidence deformation at

corresponding percentages of ore extraction for the Base Case model, shown in

Figs. 5.6(a) and 5.63, with the ore block positioned 100m shallower. A similar

minor increase in subsidence due to additional ore extraction was noted for the

models with inclined joints, BD2 and J2, presented in Figs. 5.64, 5.6(c) and 5.65.

0-100 -50-150-200-250 10050 150 200 250 300-300

(a)

BD1

100%

(b)

BD1

150%

Fig. 5.62 Subsidence at 100% and 150% for BD1 model

74°

76°


horizontal

Legend:


74°

78°

69°

90°

0°

90°

0°

MRV = 45887m3

AI = 0.95

MRV = 49966m3

AI = 0.91

163

(c)

BC

150%

Fig. 5.63 Subsidence at 150% ore extraction for Base Case model

0-100 -50-150-200-250 10050 150 200 250 300-300

(a)

BD2

100%

(b)

BD2

150%

Fig. 5.64 Subsidence at 100% (a) and 150% (b) for BD2 model

74° 67°

90°

0°

55°

69°


vertical

horizontal

Legend:


71°

71°

55°

70°

20°

70°

20°

MRV = 30424m3

AI = 0.91

MRV = 68476m3

AI = 0.87

MRV = 70465m3

AI = 0.80

164

J2

150%

Fig. 5.65 Subsidence at 150% ore extraction for J2 model

As illustrated in Fig. 5.66 for the simulations with vertical/horizontal joints, an

increase in block depth led to steeper delineating angles, where placing the block

100m deeper reduced the angles by up to 3°. Comparison of models with

inclined joints shows a more complex response. Westward from the block centre

vertical axis the delineating angle was decreased by 2°, whereas in an eastward

direction it was increased by 3°, so that the delineating angle approached the

inclination of the joints dipping into the cave.

Figs. 5.67 and 5.68, respectively, present surface profiles for models BC, BD1

and J2, BD2 at 100 and 150% ore extraction respectively. Contrasting the

maximum crater depth at 100% ore extraction for models with vertical/horizontal

and inclined joints, respectively a 37% and 50% decrease with 100m block

deepening is observed. Comparing change in the maximum crater depth with an

additional 50% ore extraction, it can be noted that for simulations with

vertical/horizontal joints a 20.3m or 36% increase in depth was observed for the

model with the ore block positioned at 200m depth (BC) and a 22.3m or 64%

increase for the block positioned at 300m depth (BD1). For the simulations with

inclined joints the corresponding changes were 32.5m or 73% (J2) and 25.6m or

116% (BD2). It can be inferred that with increase in the ore extraction volume

the subsidence crater deepens more rapidly for simulations with deeper located

blocks.

70° 53°

70°

20°

MRV = 38847m3

AI = 0.76

165

300m (3H)

200m

(2H)100m

(H)

100m (W)

300m

200m

Fig. 5.66 Comparison of surface profiles and angles limiting major surface deformations for models with varying block depth and joint inclination at 100% ore extraction

(a) BC and BD1, (b) J2 and BD2

-80

-70

-60

-50

-40

-30

-20

-10

0

-350 -250 -150 -50 50 150 250 350

Ve

rtic

al d

isp

lac

em

en

ts, m


BC 100%

BC 150%

BD1 100%

BD1 150%

0, -55

0.9, -57

0.9, -34.7

0.9, -75.3

Lowest point

coordinates, m

Fig. 5.67 Surface profiles at the end of ore extraction for BC (100%), BC (150%), BD1 (100%) and BD1 (150%) models

-80

-70

-60

-50

-40

-30

-20

-10

0

-350 -250 -150 -50 50 150 250 350

Ve

rtic

al d

isp

lac

em

en

ts, m


J2 100%

J2 150%

BD2 100%

BD2 150%

9.4, -44.5

0.9, -47.6

10.3, -22

0, -77

Lowest point

coordinates, m

Fig. 5.68 Surface profiles at the end of ore extraction for J2 (100%), J2 (150%), BD2 (100%) and BD2 (150%) models

90°

0°

(a)

70°

20°

(b)

BD1

BC

BD2

J2

74° 78°

71° 76°

55° 71°

53° 74°

166

Comparative characterization of major subsidence deformation for models BC,

BD1 and, J2 and BD2 is given in Figs. 5.69 and 5.70, respectively. For the

simulations with vertical/horizontal joints (BC, BD1) an additional 50% ore

extraction irrespective of the block depth caused an increase of about 15% in the

total extent of the zone of major surface displacements. For simulations with

inclined joints (J2, BD2) a more moderate increase of <5% was observed. It is

interesting to note that in the direction of major asymmetry the increase in the

extent of major displacements was minimal. This indicates that the limits of rock

mass mobilization limits in the dip direction of the sub-vertical joint set were

largely reached at early stages of ore extraction. Subsidence asymmetry was in

fact decreased by about 20% due to failure developing in an eastward direction,

where inclined joints are dipping into the cave. It appears that reduction in the

muck pile support due to ore extraction induced rock mass failure through rock

bridge shearing and sliding along steeply inclined joints dipping into the cave.

Increase in block depth by 100m led to increases in the total extent of major

surface displacements of up to 15 and 34 % for models with vertical/horizontal

(BD1) and inclined (BD2) joints, respectively. Subsidence asymmetry remained

virtually unchanged for model BD1 and decreased by about 30% for model BD2.

Far-field displacements for the studied models are given in Figs. 5.71 and 5.72.

Greater block depth, as well as a larger volume of extracted material, led to an

increased zone of subsidence displacements. A sharp increase in displacement

values (more than an order of magnitude) is observed for simulations with a

300m deep block. For all considered simulations, extraction of an additional 50%

of ore led to a relatively moderate increase in surface displacements and

extended the zone of 1cm displacements by up to 50m. Surface displacements

in excess of 1cm were observed as far as 200m from the caving boundary (250m

from the block centre vertical axis) for model BD1, and 300m for model BD2.

167

207234 228

252

100%

113%

100%

111%

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

To

tal e

xte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts

no

rmalized

by B

ase C

ase, %

To

tal e

xte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts,

m

BC BC BD1 BD1 150% 150%

218242 252

291

100%

111%

100%

115%

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

To

tal e

xte

nt o

f 10cm

ho

riz.

su

rface d

isp

lacem

en

ts

no

rmalized

by B

ase C

ase, %

To

tal exte

nt o

f 10cm

ho

riz.

su

rface d

isp

lacem

en

ts,

m

BC BC BD1 BD1 150% 150%

-112

95

-126

108

-128

100

-136

116116%

106%

100%

100%

114%

113%

100%

100%

-300 -200 -100 0 100 200 300

-250 -200 -150 -100 -50 0 50 100 150 200 250

Extent of 10cm surface vertical displacements in relation to block centre, normalized by BC / BD1, %


BC

BC 150%

BD1

BD1 150%

BC

BC 150%

BD1

BD1 150%

-118

100

-134

108

-136

116

-167

124107%

123%

100%

100%

108%

114%

100%

100%

-300 -250 -200 -150 -100 -50 0 50 100 150 200 250 300

-250 -200 -150 -100 -50 0 50 100 150 200 250

Extent of 10cm surface horizontal displacements in relation to block centre, normalized by BC / BD1, %


BC

BC 150%

BD1

BD1 150%

BC

BC 150%

BD1

BD1 150%

Fig. 5.69 Subsidence characterization for models BC (100%), BC (150%), BD1 (100%) and BD1 (150%) Total extent of major (≥10cm) vertical (a) and horizontal (b) surface displacements in m and in % of Base Case value; extent of 10cm surface vertical (c) and horizontal (d) displacements in relation to centre axis of the block, in m

268292

354 383

100%

109%

100%

108%

0

50

100

150

200

250

300

350

0

50

100

150

200

250

300

350

To

tal e

xte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts

no

rmalized

by J

2 / B

D2, %

To

tal e

xte

nt o

f 10cm

vert

ical

su

rface d

isp

lacem

en

ts,

m

J2 J2 BD2 BD2 150% 150%

308

324

412 425100%

105%

100%

103%

0

50

100

150

200

250

300

350

280

290

300

310

320

330

340

350

To

tal e

xte

nt o

f 10cm

ho

riz.

su

rface d

isp

lacem

en

ts

no

rmalized

by J

2 / B

D2, %

To

tal exte

nt o

f 10cm

ho

riz.

su

rface d

isp

lacem

en

ts,

m

J2 J2 BD2 BD2 150% 150%

-161

107

-169

123

-223

131

-229

154118%

103%

100%

100%

115%

105%

100%

100%

-300 -200 -100 0 100 200 300

-250 -200 -150 -100 -50 0 50 100 150 200 250

Extent of 10cm surface vertical displacements in relation to block centre, normalized by J2 / BD2, %


J2

J2 150%

BD2

BD2 150%

J2

J2 150%

BD2

BD2 150%

-201

107

-201

123

-258

154

-260

165107%

101%

100%

100%

115%

100%

100%

100%

-300 -250 -200 -150 -100 -50 0 50 100 150 200 250 300

-250 -200 -150 -100 -50 0 50 100 150 200 250

Extent of 10cm surface horizontal displacements in relation to block centre, normalized by J2 / BD2, %


J2

J2 150%

BD2

BD2 150%

J2

J2 150%

BD2

BD2 150%

Fig. 5.70 Subsidence characterization models J2 (100%), J2 (150%), BD2 (100%) and BD2 (150%) Total extent of major (≥10cm) vertical (a) and horizontal (b) surface displacements in m and in % of J2 value; extent of 10cm surface vertical (c) and horizontal (d) displacements in relation to centre axis of the block, in m

(a) (b)

(c) (d)

(a) (b)

(c) (d)

168

BD

1

BD

1

BD

1 1

50%

BD

1 1

50%

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

-300 -250 -200 -150 150 200 250 300

Vert

ical d

isp

lacem

en

ts,

m


-0.38 -0.54

B

C

BCBC

150%

BC

150%

BC

150%

BC

150%

BD

1

BD

1

BD

1

BD

1

BD

1BD

1 1

50%

BD

1 1

50%

BD

1 1

50%

BD

1 1

50%

BD

1 1

50%

0

0.05

0.1

0.15

0.2

0.25

0.3

-300 -250 -200 -150 150 200 250 300

Ho

rizo

nta

l d

isp

lacem

en

ts, m


Fig. 5.71 Total vertical (a) and horizontal (b) surface displacements at the end of ore extraction at different distances from block centre for BC (100%), BC (150%), BD1 (100%) and BD1 (150%) models

J2

J2

J2 1

50%

J2 1

50%

BD

2

BD

2

BD

2

BD

2 1

50%

BD

2 1

50%

BD

2 1

50%

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

-300 -250 -200 -150 150 200 250 300

Vert

ical d

isp

lacem

en

ts,

m


-0.6 -0.4 -1.8

J2

J2

J2

J2

J2 1

50%

J2 1

50%

J2 1

50%

J2 1

50%

J2 1

50%

J2 1

50%

BD

2

BD

2

BD

2

BD

2

BD

2

BD

2

BD

2 1

50%

BD

2 1

50%

BD

2 1

50%

BD

2 1

50%

BD

2 1

50%

BD

2 1

50%

0

0.05

0.1

0.15

0.2

0.25

0.3

-300 -250 -200 -150 150 200 250 300

Ho

rizo

nta

l dis

pla

cem

en

ts, m


-0.6-0.8 -1.8 -6.4-1.3-0.6

Fig. 5.72 Total vertical (a) and horizontal (b) surface displacements at the end of ore extraction at different distances from block centre for J2 (100%), J2 (150%), BD2 (100%) and BD2 (150%) models

(a)

(b)

(a)

(b)

169

Overall, the conducted ELFEN modelling showed that the depth of the ore block

and the volume of extracted material may influence caving induced surface

subsidence development. The assumed increase in ore block depth and higher

volume of extracted material generally led to larger subsidence deformations. The

key modelling observations can be summarized as follows:

1. An increase in the block depth from 2H to 3H did not affect the joint

orientation controlled mechanism of subsidence deformations development.

2. Simulation with vertical/horizontal joints exhibited a moderate (<0.35H)

increase in the total extent of the zone of major (≥10 cm) surface

displacements, whereas for the case with inclined joints the increase in the

total extent of major subsidence displacements was significant (> 0.5H).

3. For both assumed jointing conditions, excavation of a deeper block led to

a significant increase in extent and magnitudes of far-field surface

displacements.

4. Extraction of an additional 50% of ore block volume did not result in any

major increase in the subsidence damage, leading to relatively moderate

changes in the total extent of major subsidence deformation, with larger

accumulated damage for the case with vertical/horizontal joints.

5.9 Results Synthesis

The preceding sections presented the results of the conceptual modelling study and

outlined key modelling observations and conclusions with respect to the influence of

the individual factors. Here results of the entire conceptual study are synthesized.

Comparative summary of all conceptual simulations is given in Figs. 5.73 to 5.76,

which compare, accordingly, the total extent of major (≥10cm) subsidence

displacements, extent of major surface displacements with respect to the caving

boundaries, minimum angle of fracture initiation and asymmetry index, and

mobilized rock mass volume. A preliminary statistical summary of conceptual

modelling results is given in Appendix A.

170

Based on analysis of the conceptual modelling results a preliminary classification

of block caving induced surface subsidence for cases, where no major geological

discontinuities intersect the cave, is proposed, as shown in Table 5.2. This

classification is supplemented by a preliminary classification of the influence of

major geological discontinuities on surface subsidence, given in Table 5.8. It

should be emphasized that these classifications are based on the modelling that

assumed a rock mass corresponding to ~ MRMR 50-60, uniform ore extraction

and block depth 2H (where H is block height). The relative significance of

individual parameters is summarized in the influence assessment matrix, shown

in Table 5.9. Recognizing the fact that this matrix was developed based on

simulated variations of specific parameters it is believed that it captures overall

behavioural trends.

The proposed preliminary subsidence assessment classifications and the

parametric influence matrix are meant to aid practical engineering assessment of

potential block caving subsidence at pre-feasibility and design stages. It cannot

be over-emphasized that such assessments must be tailored to and take full

consideration of specific mine site conditions.

171

Fig. 5.73 Comparative summary of modelling results - total extent of major (≥10cm) surface displacements

172

Fig. 5.74 Comparative summary of modelling results - major (≥10cm) surface displacements asymmetry with respect to the caving boundaries

173

Fig. 5.75 Comparative summary of modelling results - minimum angles delineating the extent of major (≥10cm) surface displacements, asymmetry index

174

Fig. 5.76 Comparative summary of modelling results – volume of the rock mass mobilized by the caving

175

Table 5.8. Preliminary classification of caving induced surface subsidence for cases with no major geological discontinuities

Subsidence category

Typical subsidence deformations Associated rock mass conditions

Min angle of fracture initiation

Asymm. index

Disturbed rock mass volume in

% of ore extracted

I. Moderate

W=H

2Hhighly

disturbed torubblizedrock massdisturbed

rock mass

intact

rock mass

< 2.5H

Primary controls:

combination of vertical/sub-vertical and horizontal/sub-horizontal persistent joint sets, stronger host rock

Contributing factors:

low horizontal stress

> 70° 0.9 -1 < 220

II. Significant < 3H

Primary controls:

combination of steeply and low dipping persistent joint sets,


higher joints stiffness

55° - 70° 0.7 - 0.9 220 - 250

III. Extensive > 3.5H

Primary controls:

combination of steeply and low dipping highly persistent joint sets


high horizontal stress

< 55° < 0.7 >250

176

Table 5.9. Preliminary classification of the influence of major geological discontinuities on caving induced surface subsidence

Degree of influence

Typical subsidence deformations Description

I. Low to Moderate

I(a)

fault

highly

disturbed torubblizedrock mass

intact

rock mass

disturbed

rock mass

2H

W=H

I(b)

fault

I(a) fault located at distances exceeding 0.5H from the caving boundary

fault may act as a displacement barrier limiting rock mass movements in far-field

I(b) more than 2/3 of the fault near surface segment is located within caving zone

fault may affect caving mechanism

II. Significant to Extensive

II(a)

fault

II(b)

fault

major

block

II(a) steeply inclined (80 - 60) faults intersecting caving boundary

II(b) moderately inclined (60 - 30) faults intersecting caving boundary

in both cases extent of surface subsidence and subsidence asymmetry will be governed by fault inclination

177

Table 5.10. Initial influence assessment matrix of factors contributing to block caving induced surface subsidence

Factors Specific conditions Potential degree of influence (”+” increase, “-“ decrease) Potential worst case combinations

extent of major surface disturbances

footprint asymmetry extent of far-field displacements

1. Rock mass jointing

1(a) steeply dipping persistent sets High (+) High (+) High (+) 3(a), 4(b), 6(a)

1(b) vertical/sub-vertical persist. sets High (-) High (-) High (-)

2. Major geological discontinuities

2(a) faults intersecting caving boundary

High (+/-)1

High (+/-)1 High (+/-)

1 3(a), 4(b), 6(a)

2(b) faults located in immediate vicinity from the caving boundary

Moderate (+/-)1 Moderate (+/-)

1 Moderate (+/-)

1 3(a), 4(b), 6(a)

2(c) faults located at distances exceeding half of block height

Low (+/-)1 Low (+/-)

1 Low (+/-)

1

3. Rock mass tensile strength

3(a) lower strength Moderate (+) Low Low 1(a), 6(a)

3(b) higher strength Moderate (-) Low Low

4. Stress level 4(a) K<1 Low (-) Low (-) Moderate (-)

4(b) K>1 Low (+) Low (+) High (+) 1(a), 6(a)

5. Varying lithological domains

5(a) stronger caprock Low to High (-)

2 Low to High (-)

2 Low to Moderate (-)

2

5(b) stronger host rock

6. Block depth 6(a) block depth ≤2H (block height) Moderate (+) Low (+)2

High (-) 1(a), 2(a), 2(b), 3(a), 4(a)

6(b) block depth >2H Moderate (-) Low (-)2

High (+)

7. Extraction volume

7(a) additional 50% Low (+) Low (+) Low (+) 2(a), 3(a)

1 function of fault inclination;

2 function of prevailing joint sets inclination

178

5.10 Summary

The conducted modelling demonstrated the significant potential benefit of the

proposed FEM/DEM-DFN approach to block caving subsidence analysis. A series

of numerical experiments highlighted the importance of joint set orientation and

persistence, fault location and inclination in determining the subsidence

development mechanisms and their governing role in defining the degree of

surface subsidence asymmetry. The modelling results correlated reasonably

well with the available field observations. New insights were gained into the

complex mechanism of caving induced rock mass deformations and subsequent

subsidence development. This allowed development of preliminary block caving

subsidence classifications and a parametric influence assessment matrix aimed

to aid practical engineering analysis.

179

CHAPTER 6: BLOCK CAVING INDUCED INSTABILITY IN LARGE OPEN PIT SLOPES

6.1 Introduction

Low cost and high efficiency are making block caving an attractive option for the

continuation of mining activities at large open pit operations that otherwise are

approaching their economic limits. A few such projects have been implemented

and many more are being planned, including, but not limited to, the world largest

open pit mines, Bingham Canyon (USA) and Chuiquicamata (Chile). Recent

implementation of block caving at a large open pit mine at Palabora (South

Africa) illustrates that transition projects can be successfully carried out and

achieve targeted ore output. At the same time however, this mine encountered a

series of complex geotechnical issues, including major surface subsidence

accompanied by a massive failure of the North pit wall. This development

highlighted the need for a better understanding of the complex response of pit

slopes to caving. This chapter examines the mechanisms leading to block

caving induced failure of large open pit slopes, focusing on step-path driven

failure and also presents preliminary FEM/DEM-DFN based modelling of the

Palabora mine failure.

6.2 Transition from Open Pit to Block Cave Mining

Stacey & Terbrugge (2000) noted that in an optimum open pit operation, pit

slopes will have been designed to be very close to the limit of their stability.

Therefore the transition operation should be designed with full consideration of

the high sensitivity of large open pit slopes to caving induced disturbances.

These authors also reported a case study where pit slope design was flattened

by 5 degrees to account for a future block cave. From the open pit mining

perspective, often, the original planning did not consider future underground

180

mining, leaving little scope for steepening of slopes to avoid impact to mining

infrastructure, particularly where located in the vicinity of the pit rim. At the same

time, caving operations require high upfront investments and are very inflexible

once commenced. Considering these circumstances reliable assessment of the

interaction between the developing cave and the existing open pit becomes

important for successful adaptation of block cave mining.

According to Eberhardt et al. (2007) the rock engineering interactions involved

with transition projects are highly complex. On surface, pit wall slopes frequently

exceed heights of several hundred metres and the potential for deep-seated,

stress-controlled rock slope failures is becoming more of an issue compared to

bench-scale, structurally-controlled wedge failures. Block caving by its very

design results in an almost immediate response of the rock mass leading to

deformation and surface subsidence. Beck & Pfitzner (2008) emphasized the

forecasting and characterization of the underground - slope interaction as one of

the most challenging tasks in rock mechanics. Unfortunately, to the author‟s

knowledge, slope stability issues related to open pit - caving interaction have to

date received relatively limited attention in the published literature.

As discussed in Section 5.2.3.2, Flores & Karzulovic (2004) performed a detailed

analysis of the subsidence associated with open pit caving interaction, using the

continuum code FLAC2D and a limit equilibrium technique. Eberhardt et al.

(2007) compared application of FLAC2D and UDEC for the analysis of block

caving induced slope deformations. The results demonstrated that both the

magnitude and shape of the subsidence profile modelled can vary as a function

of modelling approach (continuum vs. discontinuum), constitutive model (elastic

vs. elasto-plastic), and geometry of the discontinuity network. The authors

indicated that one significant limitation of conventional continuum and

discontinuum numerical analyses is their inability to explicitly account for brittle

fracture processes, and their subsequent role in underground-surface mine

interactions.

181

Beck & Pfitzner (2008) suggest that the interaction between the developing cave

and the existing mine operation during cave propagation, breakthrough and draw

down need to be simulated so that the transition can be properly planned, and so

that the risks and effects of the new block caves can be properly appreciated.

These authors provide example applications of the three dimensional continuum

code ABAQUS (Simulia, 2007) to the analysis of interaction between open pit

and block cave and two neighbouring block caves. They proposed a set of

milestones to assess caving induced interaction and employed dissipated plastic

energy and plastic strain as interaction indicators.

Elmo et al. (2007b, 2008) adopted a FEM/DEM-DFN modelling methodology for

open pit - block cave interaction modelling. A series of conceptual models were

run investigating the effect of joint orientation, stress ratio and rock mass strength

on caving induced slope instability. It was found that the joint orientation may

have a defining role in caving induced slope failure. This agrees with the findings

of Salim & Stacey (2006), whose numerical modelling study has shown that

variability in the geometry of the jointing can have a major effect on the slope

behaviour, and on geometry and extent of the volume of collapse. It should be

recognized that use of large scale continuum modelling where jointing can only

be accounted for implicitly may not be applicable in all cases. Research by Elmo

et al. (2007b, 2008) illustrated that use of the FEM/DEM-DFN methodology may

provide valuable insights into complex interaction behaviour.

6.3 Characteristic Slope Failure Mechanisms in Large Open Pits

According to Franz et al. (2007) large scale rock slope failure mechanisms are not

completely understood, and may often comprise a number of different mechanisms.

As summarized by Baczynski (2000) high rock slope failures may include:

sliding on one or more major geological discontinuities (planar,

tetrahedral, active-passive wedges);

sliding along circular or quasi-circular failure paths through a highly

fractured or weak rock mass, or across rock mass fabric (rotational

failure);

182

toppling; and

composite modes, involving two or more of the above mechanisms.

Piteau & Martin (1982) stated that failure mechanisms are easiest to assess if they

can be represented two dimensionally, so that the failure surface is assumed to be

sub-parallel to the strike of the slope allowing analysis to be carried out for a unit

width of the slope. Two dimensional failure assumes the presence of lateral release

surfaces which do not provide any resistance to failure. Two-dimensional failures

which involve a single discontinuity or a single set of discontinuities are planar

failures and toppling. Rock mass failure encompassing rotational shear failure

develops when the slope is sufficiently high and steep so that the shear stress of the

rock mass is exceeded due to high stresses in the slope. It should be emphasized

that this type of failure is more characteristic of weaker materials and development

of a circular failure in strong rock is uncommon. Wedge failure is a three

dimensional phenomenon that develops when two intersecting discontinuities form a

tetrahedral block which can slide out of the rock slope. Stacey (2007) indicated that

failure mechanisms in high, hard rock slopes are much more complex than planar,

wedge and circular shear failure surface, and toppling. Progressive failure in hard

rock slopes involves initiation and progression of failure along existing weakness

planes, and initiation and progression of failure in intact rock, i.e. step-path failure

mechanism. The mechanisms described above are illustrated in Fig. 6.1. Additional

information on planar, toppling, sliding and wedge failure mechanisms in rock slopes

can be found in Wyllie & Mah (2004).

This chapter will focus on step-path failure where the contribution of intact rock

bridges to slope stability can be quite significant. As reported by Piteau & Martin

(1982) analysis carried out by Martin (1978) has shown that for slopes greater than

300m high in moderately hard rock, the occurrence of less than 10% rock bridges

(vertical spacing of rock bridges as a % of total discontinuity length) along a

prospective failure surface would provide enough resistance to shear failure to

achieve limit equilibrium.

183

Planar failure Toppling failure

Rotational shear

failureWedge failure

Step-path failure

Fig. 6.1 Slope failure modes (based on Sjöberg, 1999)

Jennings (1970) pioneered detailed step-path analyses of rock slopes with

development of a limit equilibrium approach that incorporated shear failure along

joints, shear through intact rock and tensile failure of rock bridges. To consider

continuity of jointing, coefficients of continuity and discontinuity were introduced.

The Factor of Safety (FS) was calculated based on an apparent cohesion and

friction angle on an assumed mean failure plane. Jennings (1970) also analyzed the

various modes of step-path development from upper to lower joints and the

existence of both stepped surfaces in the dip and strike directions. The work by

Jennings was further extended by Jaeger (1971). Fig. 6.2 compares the limit

equilibrium solutions for planar step path failure.

184

where: A - surface area of failure; W - sliding rock mass weight;

α - slope angle of failure; c and υ - cohesion and friction

along failure surface; Fτ and Fn - tangential and normal

forces

where: k - coefficient of continuity; ci and υi - cohesion and friction

of intact rock; cj and υj - joint cohesion and friction

where: To - intact tensile strength; β - angle of discontinuity in

step-path

Fig. 6.2 Comparison of limit equilibrium analysis of planar and step-path failure (modified after Eberhardt et al., 2004a, with permission)

Among recent developments in limit-equilibrium based solutions of step-path failure,

work by Baczynski (2000) is of particular interest. This author, based on the

research of McMahon (1979) and Read & Lye (1984) developed the STEPSIM4

code that can evaluate step-path development using probabilistic analysis. The

STEPSIM4 “step-path” method provides an avenue for assessing the statistical

shear strength along potential two-dimensional failure paths through rock masses.

A potential step-path failure surface is evaluated along a system of ground condition

“cells”. Where each “cell” is statistically associated with failure through one of

several failure modes including sliding along adverse joints, stepping up along

steeper dipping joints and direct shear through intact rock bridges. Repeating the

simulation for a large number of potential failure paths (> 2000), STEPSIM4

185

provides a statistical distribution of shear strength along critical step paths. This tool

provides a valuable and logical approach, however, it does not specifically consider

the increased importance of the stress field and deformation processes in high rock

slopes (Franz et al., 2007). Moreover, it does not consider explicitly intact rock

fracture mechanisms.

According to Stead et al. (2007) the role of brittle fracture modelling in rock slope

instability both in engineered and natural slopes is the subject of considerable on-

going research. Impetus for this work was originally derived from the failure of high

mountain slopes, however the increasing number of large open pits with projected

depths of 1 km or more has become a major driver for understanding intact rock

fracture in rock slope environments.

Recognizing the significance of the diversity of roles and scale of brittle fracture

within rock slopes, Stead et al. (2007) proposed a classification of brittle fracture

processes in rock slopes in terms of primary, secondary and tertiary processes:

Primary brittle fracture processes occur prior to onset of failure and

include (i) propagation of failure surfaces through fracture tip growth, (ii)

coalescence of fractures and failure of intact rock bridges and (iii) shearing

along discontinuities involving removal of asperities.

Secondary brittle fracture processes occur following the onset of failure

and involve (i) development of rear and lateral release surfaces leading

toward global slope failure and (ii) internal deformation, fracturing and

dilation of the rock slope mass associated with translational failure,

toppling or multiple complex interacting mechanisms.

Tertiary brittle fracture processes are associated with the final stages of

slope failure involved the comminution of the rock mass associated with

transport leading up to debris deposition.

Stead et al. (2007) emphasized the particular importance of simulation of the first

two processes for large scale failures. Simulation of rock comminution may involve

significant run-times and therefore may not be practical in all cases.

186

Numerical modelling studies that addressed primary and in some cases

secondary and tertiary brittle fracture processes in slopes include Scavia (1990,

1995), Scavia & Castelli (1996), Muller & Martel (2000), Stacey et al. (2003),

Wang et al. (2003), Eberhardt et al. (2004a,b), Stacey (2006), Stead & Coggan

(2006), Elmo et al. (2007b), Karami et al. (2007), Franz et al. (2007), Eberhardt

(2008) and Yan (2008).

Stead et al. (2007) reviewed the state-of-the art in brittle fracture modelling as

applied to both large natural and open pit slopes and illustrated several example

applications of fracture mechanics based FEM/DEM modelling, including a pit slope

proximity problem, as shown in Fig. 6.3. It has been shown that FEM/DEM

modelling may provide valuable insight into slope failure mechanisms. A particular

importance of the integration of FEM/DEM and DFN was emphasized.

Fig. 6.3 The pit-slope proximity problem: preliminary brittle fracture analysis (adapted after Stead et al., 2007, with permission)

187

6.4 Conceptual Study of Block Caving Induced Step-path Driven Failure in Large Open Pit Slope

6.4.1 Modelling Methodology

To investigate step-path development mechanisms during block caving - open pit

interaction a series of conceptual ELFEN models were run.

As illustrated in Fig. 6.4, a simplified 2D model geometry of a 750m deep open pit

with 50o slopes and the caving operation located 400m beneath the pit was adopted.

It was assumed that the rock mass fabric forms a potential failure surface consisting

of non-coplanar step path joints dipping into the cave and intact rock bridges with a

vertical spacing of 15m. Cave mining induced development of step-path failure was

analyzed. For the purpose of the present analysis, fracturing was allowed only within

the areas of rock bridges and in the cave itself. A fine mesh was adopted for the

fracturing regions, i.e. 2m within the cave and 0.7m for the rock bridges. Modelling

adopts the same ore extraction methodology as described in Section 4.5.1.1 and

employs the calibrated equivalent continuum properties, same as in Chapter 5, for

the cave and intact rock properties for the rock bridges. GSI based equivalent

continuum properties were adopted for area adjacent to the caving footprint, e.g.

open pit slopes. Modelling input parameters are presented in Table 6.1.

Conceptual modelling was focused on the analysis of the effect of varying:

rock bridge strength;

joint cohesion;

number of rock bridges.

Table 6.2 shows the model runs undertaken. To capture the full picture of the

interaction mechanisms a “total interaction” analysis was adopted relating cave

propagation, stress redistribution in the crown pillar with step-path failure

development and surface subsidence. History points (see Fig. 6.4) were placed at:

the footwall and hanging wall edges of the surface outcrop of the

discontinuities, where differential XY displacements (similar to Fig. 5.29)

were monitored;

188

the centres of rock bridges, where variation of shear stress was tracked;

50m below the pit bottom, where variation of vertical stress was tracked.

2200m

4000m

60o

Fracturing

regions

50o

300m 300m

400m

750m

75m

RB600

RB300

10 excavation stages

60o

history point

Fig. 6.4 Typical model geometry for simulation of block caving induced step-path failure (cases with two rock bridges shown).

Equivalent continuum

History point

RB300 – rock bridge located 300m away from the cave footprint

189

Table 6.1 Modelling input parameters used in conceptual modelling

Parameter Unit

Value

Ore Open pit slopes1

GSI 70

Intact rock bridge

Rock properties

Young‟s Modulus, E GPa 18 44 60

Poisson‟s ratio, 0.25 0.25 0.25

Density, ρ kgm-3 2600 2600 2600

Tensile strength, t MPa 1 0.88 10

Fracture energy, Gf Jm-2 60 60 60

Cohesion, ci MPa 4.7 6.6 20

Friction, i degrees 45 45 50

Dilation, ψ degrees 5 5 5

Discontinuities

Fracture cohesion, cf MPa 0

Fracture friction, f degrees 35

Normal penalty, Pn GPa/m 2

Tangential penalty, Pt GPa/m 0.2

Stress level

In-situ stress ratio, K 1 1

GSI based properties were established using the RocLab v1.031 program (Rocscience Inc., 2007), assuming

mi=15, D=0 and intact rock properties σci=127MPa, Ei=60GPa

Table 6.2 Modelling scenarios

Scenario Number of rock bridges / rock

bridges %

Rock bridges tensile strength, MPa

Step-path discontinuities cohesion, MPa

M1 2 / 4 10 0

M2 2 / 4 15 0

M3 2 / 4 10 0.5

M4 3 / 6 10 0

M5 4 / 8 10 0

190

6.4.2 Modelling Results

Block caving and associated development of step-path failure in the open pit for

model M1 is illustrated in Fig. 6.5. The open pit is stable prior to caving, after which

progressive caving initiates stress redistribution within the slope hence triggering

failure of the rock bridges. The failure is initiated at the rock bridge RB600 located

furthest from the caving footprint and with some delay steps through the second

rock bridge RB300. Fig. 6.6 shows the concentration of the tensile stresses in the

rock bridges prior to fracturing and Fig. 6.7 illustrates characteristic development of

fracturing within the rock bridges. The rock bridges fail in shear, where initially the

formation of en-echelon fracturing is observed parallel to the orientation of the

major principal stress, followed by the coalescence of these fractures to form a

shear failure plane. A combined stress/displacement analysis of caving/open pit

interaction is shown in Fig. 6.8. The lower graph describes the rock mass response

below the pit bottom and shows cave propagation expressed in crown pillar

thickness and the change in vertical stress with continuous caving at a history point

located 50m below the pit bottom. The upper graph illustrates the response in the

open pit slope, showing change in shear stress in the rock bridges (normalized by

the value at the end of pit excavation before caving is initiated) and differential

displacements at the surface outcrop.

Fig. 6.8 clearly shows that the surface subsidence in the open pit wall is directly

related to caving. When the thickness of the crown pillar is reduced down to

approximately 175m, a rapid destressing in the crown pillar is initiated; this causes an

unloading of the pit slope toe allowing movements within the slope, which trigger

failure of the RB600 rock bridge. Interestingly, this rock bridge fails at a very low level

of destressing, i.e at about a 3% vertical stress decrease (in relation to the stress

level at the end of pit excavation). It can clearly be seen that on failure of the rock

bridge RB600 the shear stress in the RB300 rock bridge rapidly increases and this

rock bridge then fails at about 16% vertical stress decrease in the crown pillar.

Failure of the RB600 rock bridge is associated with a distinctive drop in the

differential displacements at the location of the surface outcrop of step-path

discontinuities. Failure of the lower rock bridge occurs when accumulated differential

191

displacements reach about 3cm. It should be noted that the slope of the surface

displacement follows quite closely the variation in the crown pillar vertical stress.

end of pit excavation progressive caving

RB600 failure RB300 failure

Fig. 6.5 Block caving induced step-path failure in large open pit slope (model M1)

RB600

RB300

remaining crown pillar thickness

192

Fig. 6.6 Maximum principal stress contours (Pa) - tensile stress concentrations (red) in rock bridges prior to failure

Fig. 6.7 Typical rock bridge failure development

193

-0.2

-0.15

-0.1

-0.05

0

-5

0

5

10

15

20 22 24 26 28 30 32 34 36

RB600

RB300

differential XY displ. at

surface outcrop

0

50

100

150

200

250

300

350

400-15

-10

-5

0

σyy (50m below pit bottom)

crown pillar thickness, m

No

rm. sh

ea

r str

ess X

Y, M

Pa

Ve

rtic

al s

tre

ss Y

Y, M

Pa

ΔX

Y d

isp

l. a

t su

rfa

ce

ou

tcro

p, m

Cro

wn

pill

ar

thic

kn

ess, m

simulation time, num.sec


end o

f pit e

xcavation

Fig. 6.8 Stress/displacement analysis of caving - open pit slope interaction (rock bridges failure, model M1)

Model M2, in which the tensile strength of the rock bridges was increased by

50% shows generally a similar step-path failure development as in Model M1,

Fig. 6.5. Comparing Figs. 6.8 and 6.9, it should be noted that increasing the rock

bridge tensile strength did not result in a significant change in the simulated

response, showing only slightly more brittle behaviour, i.e. the failure of the upper

and lower rock bridge was initiated at about 2 and 12% of crown pillar

destressing, respectively. It appears that for the given step-path arrangement of

joints the magnitude of the tensile strength increase was not sufficient to alter the

overall failure process. Contrasting models M1 and M3 (Figs. 6.8 and 6.10) it is

evident that even assumption of a moderate cohesion of 0.5MPa along the

discontinuity surfaces can affect the step-path failure development quite significantly.

Failure of the upper and lower rock bridges occurs nearly simultaneously at about

18% crown pillar destressing. It appears that cohesion on the discontinuities

provides a load distribution link between the rock bridges and therefore they react to

the slope unloading more as a system rather than individually.

194

-0.20

-0.15

-0.10

-0.05

0.00

-5

0

5

10

15

20 22 24 26 28 30 32 34 36

RB600

RB300


surface outcrop

0

50

100

150

200

250

300

350

400-15

-10

-5

0



No

rm. sh

ear str

ess

XY

, M

Pa

Ve

rtic

al s

tre

ss Y

Y, M

Pa

ΔX

Y d

isp

l. a

t su

rfa

ce

ou

tcro

p, m

Cro

wn

pill

ar th

ickn

ess, m



Fig. 6.9 Stress/displacement analysis of caving - open pit slope interaction (rock bridge failure, model M2)

-0.20

-0.15

-0.10

-0.05

0.00

-5

0

5

10

15

20 22 24 26 28 30 32 34 36

RB600

RB300

differential XY displ. at surface

outcrop

0

50

100

150

200

250

300

350

400-15

-10

-5

0



Norm

. shear str

ess

XY

, M

Pa

Vert

ical s

tress Y

Y, M

Pa

ΔX

Y d

ispl. a

t surf

ace o

utc

rop, m

Cro

wn

pill

ar th

ickn

ess, m



Fig. 6.10 Stress/displacement analysis of caving - open pit slope interaction (rock bridge failure, model M3)

195

Models M4 and M5 assumed three and four rock bridges, respectively, as shown

in Fig. 6.11 and 6.12. For model M4, failure initiated in the upper portion of the

slope where a single rock bridge (RB600) provided limited shearing resistance,

then the failure subsequently stepped through the rock bridges located in the

lower portion of the slope (RB300 and RB150). For model M5 failure started in

the middle of the slope (RB300), stepped down to the lowest rock bridge (RB150)

and stepped up along the upper rock bridges (RB450 and RB600). It appears

that such complex step-path development patterns can be explained as follows:

the RB300 rock bridge is experiencing the highest concentrated loading from the

portion of the slope undercut by the step-path joints, and given that the shearing

resistance is nearly evenly distributed between the upper and lower portions of

the slope, the failure must be initiated at the rock bridge experiencing the

maximum loading. Subsequent failure of the lower rock bridge is related to

continuous toe unloading and hence reduced shearing resistance in the lower

portion of the slope. The upper portion of the slope is then effectively pulled

downwards by the weight of the failing slope.

As follows from Fig. 6.13, the step-path failure for simulation M4 initiates at 87%

and fully develops by 90% of crown pillar destressing, RB600 and RB300 rock

bridges fail nearly simultaneously, and the RB150 rock bridge fails with some

delay. The latter is associated with accumulated differential displacements of the

sliding block at surface of about 5cm and the rapid build up of shear stresses

within the rock bridge. According to Fig. 6.14, the step-path failure for model M5,

with four rock bridges, was initiated at 95% crown pillar destressing and

continued crown pillar collapse (see Fig. 6.12). For this model no substantial

surface subsidence was observed prior to the failure of the last rock bridge

(RB600).

196

Fig. 6.11 Block caving induced rock step-path failure in large open pit slope (model M4)

RB600

RB300

RB150

197

Fig. 6.12 Block caving induced step-path failure in large open pit slope (model M5)

RB300

RB150

RB450

RB600

198

-0.20

-0.15

-0.10

-0.05

0.00

-5

0

5

10

15

20 22 24 26 28 30 32 34 36

RB600

RB300

RB150


surface outcrop

0

50

100

150

200

250

300

350

400-15

-10

-5

0



RB300

Norm

. shear str

ess X

Y, M

Pa

Vert

ical s

tress Y

Y, M

Pa

ΔX

Y d

ispl. a

t surf

ace o

utc

rop, m

Cro

wn p

illar

thic

kness, m


RB150

RB

600 f

ailu

re

RB

300 f

ailu

re

RB

150 f

ailu

re


-0.2

-0.15

-0.1

-0.05

0

-5

0

5

10

15

20 22 24 26 28 30 32 34 36

RB600

RB450

RB300

RB150

differential XY displ.

at surface outcrop

0

50

100

150

200

250

300

350

400-15

-10

-5

0



RB600

RB300

Norm

. shear str

ess X

Y, M

Pa

Vert

ical s

tress Y

Y, M

Pa

ΔX

Y d

ispl. a

t surf

ace o

utc

rop, m

Cro

wn p

illar

thic

kness, m

simulation time, num. sec

RB150

RB450

RB

300 f

ailu

re

RB

150 f

ailu

re

RB

450 f

ailu

reR

B600 f

ailu

re


199

Fig. 6.15 summarizes the interrelationship between block caving, expressed in

reduction of thickness and destressing of the crown pillar, and the step-path failure

response (expressed as failure of the first and last rock bridges) based on models

with different percentages of rock bridges: 4 (M1), 6 (M4) and 8% (M5). The

percentage of the rock bridges relates the sum of the rock bridges spacing to the

total length of step-path forming discontinuities. It is evident that with increase in

percentage of the rock bridges along the step-path failure surface the degree of

crown pillar destressing needed to mobilize the failure increases. It appears that

the simulation with 8% rock bridges approaches the limiting equilibrium condition,

the failure development becomes less sensitive to crown pillar behaviour and is not

fully realized until complete crown pillar collapse. This agrees well with the

equilibrium threshold of 10% proposed by Martin (1978), as discussed in Section

6.3.

-100

-80

-60

-40

-20

0

0

20

40

60

80

100

2 4 6 8 10

Cro

wn

pill

ar

de

str

essin

g, %

Re

ma

inin

g c

row

n p

illa

r

thic

kn

ess , %

% rock bridges

destressing, %

thickness, %

crown pillar:

step-path failure:

first rock bridge failure

last rock bridge failure

Fig. 6.15 Development of step-path failure in the open pit slope during caving mining with relation to crown pillar geometry and stress level for simulations with different % of rock bridges in step-path failure surface

Fig. 6.16, which compares variation of vertical stress in the crown pillar (at 50m

depth below pit bottom) for studied scenarios, indicates that there is an

interrelation between the stress level in the crown pillar and the number of rock

200

bridges in the step-path failure surface. Simulation with more than two rock

bridges (M4, M5) exhibit lower stress levels in the crown pillar at the end of the pit

excavation, as well as a quite different stress unloading behaviour during caving.

Generally, a larger number of rock bridges is associated with lower stresses in the

crown pillar. Fewer rock bridges result in more rapid stress changes during

unloading. It appears that higher shearing resistance in the slope related to a

higher number of rock bridges reduces the active pressure of the slope onto the

crown pillar and vice versa. This may have implications on the manner of crown

pillar collapse. A weaker slope may impose higher stress in the crown pillar which

may in turn delay the cave propagation and therefore increase a risk of rapid

crown pillar collapse. Evidently the mechanisms of large open pit slope - caving

interactions are highly complex. The open pit rock mass competency may

influence the crown pillar response and affect cave propagation behaviour and in

turn the caving induced unloading of the open pit influences open pit slope

stability.

-15

-10

-5

0

20 22 24 26 28 30 32 34 36

M1 M2 M3

M4 M5

Simulation time, num.sec

Ve

rtic

al s

tre

ss Y

Y, M

Pa

Fig. 6.16 Variation of vertical stress in the crown pillar (50m below pit bottom) for models M1-M5

6.4.3 Conclusions

Conceptual ELFEN modelling has illustrated the potential application of

FEM/DEM modelling to the analysis of primary fracture processes within an open

pit slope during block caving. The proposed “total interaction” analysis approach

has allowed an improved understanding of the interaction mechanisms and the

two rock bridges three rock bridges

four rock bridges

201

establishment of correlations between percentage of rock bridges within the step-

path failure surface and caving induced deformations. The following section

applies a combined FEM/DEM-DFN methodology to the analysis of primary and

secondary brittle fracture processes associated with the block caving induced

open pit wall failure at Palabora mine.

6.5 Preliminary Modelling of Block Caving Induced Failure of the North Wall, Palabora mine

6.5.1 Problem Description

6.5.1.1 Background Information

Palabora mine, located in Limpopo province of South Africa is one of the

steepest and deepest large open pits in the world. Open pit mining at Palabora

commenced in 1966 at a rate of 30,000 tonnes per day (tpd) increasing to 82,000

tpd prior to closure in 2002. In total about 960 Mt of ore and 1,300 Mt of waste

were mined. Surface dimensions of the oval shaped open pit are near 1650 m in

the north-south direction and about 1950 m in the east-west direction. The pit is

approximately 800 m deep with interramp slope angles ranging from 37° in the

upper weathered lithologies to about 58° in the competent constrained ground

toward the base of the pit (Moss et al., 2006; Piteau Associates, 2005).

In 1996 a feasibility study was completed for a block cave targeting a block

height of around 500m and an ore reserve in excess of 220 Mt of carbonatite ore

at 0.7% copper. Target production was 30,000 tpd which translates into a life of

mine of about 23 years (Pretorius & Ngidi, 2008). Upon completion of major

open pit operations, a cave with a footprint of 150 to 300 m north-south and

about 700 m east-west was initiated approximately 400 m below the pit floor, as

shown in Fig. 6.17. For a short period of time, simultaneous open pit scavenging

and caving mining activities were in place (Piteau Associates, 2005).

202

Fig. 6.17 3D view of Palabora pit and cave mine (adapted after Brummer et al., 2005, with permission)

6.5.1.2 Geological Settings

The Phalaborwa Igneous Complex, 8 km long and 3.2 km wide, consists of a

succession of subvertical pipe-like bodies of alkaline and ultramafic rocks which

have intruded the surrounding Archean granite. The Palabora copper orebody

occurs in the Loolekop pipe near the center of the complex. In plan view it

represents an elliptical zone some 1.4 km long and 0.8 km wide elongated in an

east-west direction. This pipe is a composite vertical intrusion with an elliptical

interbanded configuration in which the component rock types were emplaced in

the pyroxenite host. Micaceous pyroxenite, the first intrusion, was in turn

intruded by foskorite and banded carbonatite. Late stage fracturing and forceful

intrusion resulted in emplacement of a transgressive carbonatite body at the

centre of the pipe. Most copper, iron and other ore mineralization occurs within

the foskorite and carbonatite (Piteau Associates, 1980). Detailed descriptions of

the regional and local geology can be found in Hanekom et al. (1965).

Fig. 6.18 illustrates the geological units encompassed by the Palabora open pit

boundaries as well as the pit slope geometry. A brief description of the rock units

present in the North wall is given in Table 6.3.

203

Table 6.3 Description of rock units present in the North Wall (based on FLUOR, 1994; Piteau Associates, 2005)

Rock type Description UCS, MPa

RMR

Carbonatite Forms the lower benches of the pit wall, primarily comprised of magnesium calcite with variable amount of magnetite and accessory minerals

127 61

Foskorite Positioned in the lower middle part of the pit wall and comprised of serpentinized olivine, magnetite, apatite and some phlogopite

90 56

Micaceous pyroxenite

Occupies the upper half of the pit wall, and comprises mainly of diasporite, phlogopite and accessory minerals

86 59

Structural geology at the site comprises a number of sub-vertical dolerite dykes

trending north-easterly and intersecting the complex and four major faults, as

shown in Fig. 6.19. As reported by Piteau Associates (2005) the detailed

mapping carried out at the site found eight pronounced discontinuity sets in the

pit, of which three steeply dipping sets with dip/dip direction 80o/320o, 82o/270o

and 85o/020o are present throughout the pit. In the upper portion of the pit wall a

more representative orientation of the 85o/020o set is 80o/225o (Piteau Associates,

2005). Mapping data presented by Martin et al. (1986) indicates the presence of a

sub-horizontal set 014o/07o in carbonatite, foskorite and micaceous pyroxenite.

Piteau Associates (1980) showed that the joint sets at Palabora are reasonably

consistent with depth over the mapped area and noted that joints in foskorite and

pyroxenite, which are located at increasing distance from the centre of the

orebody, have more diffuse populations and lower intensities for the peak values

compared to the carbonatite rocks.

204

Fig. 6.18 General geology and pit slope geometry at Palabora mine (adapted after Moss et al., 2005, with permission)

Legend:

MPY - micaceous

pyroxenite

FOSK - foskorite

GLM - glimmerite

FEN - fenite

CARB - carbonatite

DOL - dolerite

Fig. 6.19 Major geological structures at Palabora mine (based on data provided by Palabora Mining Company Limited)

205

6.5.1.3 North Wall Failure

As noted by Brummer et al. (2005), concurrent with the cave breakthrough into the

pit floor in late 2003 and early 2004, failure of major portion of the North wall became

apparent. Moss et al. (2006) described the open pit failure development as follows:

“Movement of all pit walls increased substantially upon cave

breakthrough into the bottom of the pit. The greatest amount

occurred in the North Wall where cumulative movements of in

excess of 1.5m were measured. The first indication of a major

problem, however, was a bench failure adjacent to one of the pit

sumps. This was followed by the discovery of large cracks some

250m back from the pit rim (note: it is not known if the cracking

occurred before or after the initial bench scale failures as only once

the failure occurred was a survey made of the dense bush that

surrounds that potion of the pit). The failure grew in size until after

a period of about 18 months it encompassed a major section of the

North Wall with the crest some 50 m back from the pit rim and the

toe somewhere near the original pit floor. The failure dimensions

were some 800 m high by 300m along the wall.”

Photographs of failure development are given in Appendix C. The failure impacted

several segments of the mine‟s infrastructure that had to be relocated including

access and haul roads, tailings, water and power lines, water reservoirs and a

railway line. Pretorius & Ngidi (2008) note that an estimated 130 million tons of

waste material failed into the open pit and that the failure resulted in a reduction in

life of the mine with potential loss of reserves of up to 30%. A plan view of the

failure, as well as the major joint sets are shown in Fig. 6.20. It can be seen that

the failure boundaries are generally defined by the major discontinuity sets.

As indicated by Pretorius & Ngidi (2008) modelling of the open pit - cave interaction

carried out by external consultants prior to the failure event concluded that pit walls

are to be stable above approximately the middle of the pit depth. Following the

failure, a back analysis was carried out by Piteau Associates (2005) using the limit

206

equilibrium package SLIDE (RocScience, 2007), and by Itasca (2005) using 3DEC

simulations (Brummer et al., 2005). The limit equilibrium study did not explain the

mechanisms leading to the North Wall failure, it was recognized that this type of

analysis has a limited ability to simulate rock mass deformations due to caving.

Brummer et al.‟s (2005) 3DEC models were constructed in order to calibrate the

properties of the rock mass with the monitored displacement, to match the failure

mode of the North wall, and to predict the likely long-term stability of the pit walls.

This study concluded that movement and deterioration of the North Wall was directly

linked to the block cave mining. Itasca (2005) concluded that: “The stability of the

North wall is controlled by joint sets. The single on-site estimated joint set of

75o/250o (dip/dip direction) produces a failure mode that matches the failure zone. A

more detailed model based on the two mapped sets 80o/140o and 80o/225o also

matches the failed zone”. Brummer et al. (2005) indicated that the deep seated

failure of the North Wall is possible if the ore is to be extracted from the caving area.

A

A

Fig. 6.20 Plan view of North Wall failure at Palabora mine

207

Assessing the possible role of major geological structures in the failure, Brummer

et al. (2005) stated that there were no combinations of major structures that

would delineate a slope failure with a dip or plunge flatter than about 66°, with

most structural combinations having a dip or plunge of at least 75°. There are no

combinations of major structures that dip or plunge to the south.

Analysis of the North Wall displacements carried out by Piteau Associates (2005)

showed that the displacements within some areas of the main zone of instability

have approached the plunge of the line of intersection of two discontinuity sets

that appear to control the stability of the North Wall. At the same time, the line of

intersection at the northern limit of the failure zone does not appear to intersect

the block cave footprint. This indicates that North Wall failure probably involved

a complex mechanism, primarily governed by the dominant rock mass fabric with

elements of brittle intact rock fracture and step-path failure.

6.5.2 General Approach in the Current Modelling Analysis

The modelling presented here is not intended to be a rigorous back analysis of

the Palabora failure and makes no attempt to exactly match the observed

deformations and associated pit slope displacements. Instead a conceptual

modelling approach is adopted which is founded on the engineering judgement

based assessment of the site geotechnical conditions with a full consideration of

the limited data available. The analysis focuses on understanding the general

principles of open pit - caving interaction and associated failure mechanisms

using the Palabora geometry as input.

Analysis of the extent of the Palabora North wall failure indicates that the failure

boundaries are largely defined by three joint sets mapped at the site. It appears

that a combination of 80o/320o and 82o/270o sets contributed to the formation of

the lateral failure release and 80o/225o (85o/020o) influenced the formation of the

rear release surface. The depth of the failure surface and the mechanism of

failure development remain uncertain. As previously stated step-path failure was

likely a major factor in the formation of the basal failure surface.

208

Notwithstanding the complexity and inherent 3D nature of the North Wall

deformations, it is believed that utilization of FEM/DEM-DFN technique even in

2D may help to provide better understanding of the failure mechanics. The

analysis presented here assumes that lateral release conditions exist a priori and

investigates formation of the basal failure plane.

6.5.3 Model Setup

Based on the interpretation of jointing data (from detailed line mapping) reported

by Piteau Associates (1980) and Martin et al. (1986) a preliminary FracMan DFN

model of part of the North Wall situated within the failure zone, corresponding to

cross-section A-A in Fig. 6.20, was generated, shown in Fig. 6.21. It was

assumed that the density of the jointing decreases away from the orebody. DFN

model input parameters are given in Appendix B. Here it should be emphasized

that the DFN model presented in Fig. 6.22 is preliminary and is based on the best

estimate of the actual jointing conditions. Ongoing work based on

photogrammetry is being conducted to refine the DFN. Due to limited available

data, it was not possible to carry out a comprehensive DFN validation analysis.

The DFN model was imported into the ELFEN model, shown in Fig. 6.22.

The mesh resolution was optimized with respect to the computing resources

available, resulting in a 2m mesh within the caving boundaries and a graded mesh

of up to 5m in the open pit slope. The modelling adopts the same ore extraction

methodology as described in Section 4.5.1.1. As evident from Table 6.3 all three

rock mass domains represented in the North Wall have a very similar rock mass

rating. For the purpose of the current analysis it was assumed that the rock mass

has uniform characteristics which are based on calibrated material properties as in

Chapter 5. To account for decreasing joint density away from the orebody, tensile

strength in the foskorite and micaceous pyroxenite was increased. Two cases

were considered:

Model P1 with a tensile strength increase of 100 and 150% in the foskorite

and micaceous pyroxenite, respectively; and

209

Model P2 with a similar tensile strength increase of 150 and 200%.

The input parameters adopted for the modelling are given in Table 6.4.

Fig. 6.21 Preliminary DFN model of Palabora mine North Wall section (a) 3D DFN model; (b) fracture traces on traceplane1

1 - assistance of Dr. Davide Elmo with generation of DFN model is gratefully acknowledged

(a)

(b)

210

3300m

9000m

Ca

rbo

nati

te

Fo

sk

ori

te

Mic

ac

eo

us

Pyro

xe

nit

e

800m

16 excavation stages

200m

400m

Fig. 6.22 ELFEN model of Palabora mine NW-SE section (section A-A in Fig. 6.20).

211

Table 6.4 Modelling input parameters for preliminary Palabora failure simulation

Parameter Unit

Value

Micaceous Pyroxenite

Foksorite Carbonotite

Rock properties

Young‟s Modulus, E GPa 18 18 18

Poisson‟s ratio, 0.25 0.25 0.25

Density, ρ kgm-3 2600 2600 2600

Tensile strength, t MPa 2 (P1)

2.5 (P2)

1.5 (P1)

2 (P2)

1 (P1)

1 (P2)

Fracture energy, Gf Jm-2 60 60 60

Cohesion, ci MPa 4.7 4.7 4.7

Friction, i degrees 45 45 45

Dilation, ψ degrees 5 5 5

Discontinuities

Fracture cohesion, cf MPa 0

Fracture friction, f degrees 35

Normal penalty, Pn GPa/m 2

Tangential penalty, Pt GPa/m 0.2

Stress level

In-situ stress ratio, K 1

6.5.4 Modelling Results and Discussion

Figs. 6.23 and 6.24 illustrate caving induced slope deformations for model P1 at

cave breakthrough and at 40% ore extraction. It can be seen that at cave

breakthrough slope failure is initiated. Caving induced slope unloading led to

mobilization of the lower portion of the slope where significant fracturing is

observed, this agrees well with the field observations. Fig. C1 (Appendix C)

illustrates caving induced failure along several benches at estimated cave

breakthrough. Initial step-path fracturing in the upper portion of the slope, as well

as formation of the tensile cracks in the open pit slope and at the pit crest, was

also observed. The basal failure surface that encompasses the entire pit slope

did not fully develop until about 40% ore extraction. As shown in Fig. 6.24 this

failure surface is step-path driven and is strongly defined by the rock mass fabric.

212

The failure outcrop at the pit crest over predicts the location of the actual failure,

by about 50m. It should be noted that this is not a significant margin given the

scale and complexity of the problem. The portion of the slope defined by the

failure surface is split into three major segments: the lower segment mobilized at

the cave breakthrough fully lost its structural coherence, while the upper

segments sustained generally minor damage.

Caving induced slope deformations at cave breakthrough and at 40% ore

extraction for model P2 are given in Figs. 6.25 and 6.26, respectively. In contrast

to model P1, here full scale slope failure did not materialize. The lower portion of

the slope mobilized at cave breakthrough, continuing to disintegrate and unravel

with ore extraction. Only minor fracturing within the slope, insufficient to form a

failure surface, was observed. This highlights the sensitivity of the modelling

outcome to the assumption of the pit slope rock mass strength.

Due to very long run-times the modelling was terminated at about 80% ore

extraction, with no changes in the observed deformation trends. In general,

models P1 and P2 illustrated quite different outcomes which could lead to very

different implications in terms of mine planning. The uncertainty in the modelling

input parameters and overall limited understanding of the strength of the rock

mass at a large open pit scale pose an important dilemma for decision makers.

Overall the conducted analysis of North Wall jointing conditions, observed

deformations and the conducted modelling suggest that failure of the North Wall

was largely governed by rock mass fabric. The in-situ conditions provided the

means to enable the formation of lateral and rear release surfaces as well as

formation of a step-path driven failure surface. The analysis showed that when

based on sound engineering judgement, even with limited data, FEM/DEM-DFN

modelling can contribute to the development of understanding of complex failure

mechanisms related to open pit - caving interaction. It appears that FEM/DEM-

DFN technique can be successfully employed for analysis of practical interaction

problems.

213

approximate failure

crest location

Fig. 6.23 Pit slope deformation at cave breakthrough for model P1

98 m

approximate failure

crest location

Fig. 6.24 Pit slope deformation at 40% ore extraction for model P1

214

approximate failure

crest location

Fig. 6.25 Pit slope deformation at cave breakthrough for model P2

approximate failure

crest location

Fig. 6.26 Pit slope deformation at 40% ore extraction for model P2

215

6.5.5 Conclusions

Transition from open pit to underground mining at Palabora mine presents an

important example of the pit wall instability triggered by caving operations. Using a

combined FEM/DEM-DFN modelling approach it was possible to investigate the

formation of the basal failure surface within the open pit slope as a direct result of

caving. The modelling highlighted the importance of open pit slope strength and its

influence on caving induced slope response. It appears that in open pit - caving

transition projects, reliable estimates of open pit slope strength is equally important

to the assessment of the role of major geological structures. It is however realized

that establishing geomechanical parameters for large open pits remains a challenge

yet to be resolved.

In the author‟s opinion the modelling of complex interaction problems requires

careful consideration of site specific conditions, including, but not limited to, rock

mass strength, rock mass fabric and loading/unloading conditions. Given the

uncertainties associated with the development of major transition projects a

range of possible conditions should be considered, including varying

assumptions of rock mass strength, variability of jointing orientation and

persistence, as well as different possibilities of caving development (slope

unloading conditions). Considering the importance of the implications of design

errors the additional effort to carry out detailed numerical modelling analysis

using techniques capable of capturing the problem complexity is without doubt

justifiable. Such exercise may be time consuming given the current reliance on

single processor computing capabilities. It is however anticipated that further

code improvements and use of computing clusters will enable comprehensive

modelling analysis of interaction problems in a timeframe acceptable for practical

engineering design.

6.6 Summary

This chapter investigated the interrelation between caving mining and open pit slope

stability. The proposed “total interaction” analysis related the destressing of the

216

crown pillar due to caving with unloading induced failure within the slope and the

resultant subsidence at the surface. Analysis indicates that there is a threshold of

critical intact rock bridge percentage along the step-path failure plane that may

ensure stability of the open pit throughout caving operations. A preliminary analysis

of the Palabora mine case study indicates that the formation of a step-path driven

basal failure surface within the pit slope rock mass fabric is plausible. Modelling

highlighted the sensitivity of the results to the assumed rock slope tensile strength.

Notwithstanding, this research has demonstrated that comprehensive FEM/DEM-

DFN modelling provides a promising technique for the analysis of highly complex

rock engineering problems. This is particularly encouraging in light of the future

need for reliable design tools for underground – open pit transition projects.

217

CHAPTER 7: CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER RESEARCH

7.1 Conclusions

Increasing use of block caving mining methods and ever increasing ore

extraction volumes are posing the questions of the effect of caving mining at the

surface and the implications of surface subsidence on mining activities, the

environment and socio-economics. The assessment of caving subsidence

phenomena is one of the most challenging tasks in mining geomechanics.

7.1.1 Current State of Knowledge of Block Caving Induced Subsidence

A comprehensive literature review carried out as part of the current study has shown

that our knowledge of rock mass behaviour leading to surface subsidence in block

caving settings is rather tentative and primarily founded on empirical, mostly

qualitative, observations. This is perhaps not surprising given the scale of the block

caving problem, the complexity of rock mass response and the multitude of factors

affecting subsidence. The literature focuses on the importance of the effect of

geological discontinuities in subsidence development, stopping short of elaborating

on the effect of other factors. Available methods of subsidence analysis include

empirical, analytical and numerical approaches. Empirical methods are not

particularly reliable. Analytical approaches are restrictive, and being based

principally on Hoek‟s (1974) assumed failure mechanism, are able to provide only

estimates for the angle of break. Numerical approaches being inherently more

flexible and sophisticated offer an opportunity to improve our understanding of block

caving subsidence phenomena and increased accuracy of subsidence predictions.

However, previous modelling studies have been largely directed toward providing

subsidence predictions for a particular site. The modelling study by Flores &

Karzulovic (2004) was the first attempt after Laubscher (2000) to provide non-site

218

specific guidance for subsidence analysis. It should be noted that their modelling

was limited to the case with an open pit and no consideration was given to the

effects of significant factors including rock structure. It appears that to date no

comprehensive attempt has been undertaken to evaluate the general principles

characterizing surface subsidence development in block caving settings and the

predominant factors governing subsidence phenomena.

7.1.2 FEM/DEM-DFN Approach to Subsidence Analysis

Block caving subsidence is a product of a complex rock mass response to

caving. This response comprises massive brittle fracture driven failure of the

rock mass both in tension and compression, along existing discontinuities and

through intact rock bridges. Moreover, block caving subsidence development

almost invariably involves complex kinematic mechanisms. It appears that

realistic simulation of the subsidence phenomena necessitates consideration of

fracture mechanics principles for brittle fracturing simulation and a blend of

continuum and discontinuum approaches to capture the complex failure

mechanisms. The current study adopted a state-of-the-art hybrid continuum-

discontinuum approach based on finite/discrete element method (Munjiza et al.,

1995) and incorporating fracture mechanics principles, implemented in the

proprietary code ELFEN (Rockfield Software Ltd., 2006). This code has been

extensively validated and widely applied to the analysis of a variety of rock

engineering problems.

Vyazmensky et al. (2007) evaluated various approaches to rock mass

representation within a FEM/DEM framework and concluded that explicit

consideration of discontinuities in block caving subsidence modelling is essential.

Therefore, the mixed discrete fracture network/equivalent continuum approach to

rock mass representation was utilized, where the rock mass is represented as an

assembly of spaced discontinuities and intervening regions with reduced intact

properties, the latter being scaled to incorporate the weakening effect of smaller

scale discontinuities not explicitly included in the model. The geologically sound

representation of discontinuities was achieved by employing DFN modelling,

219

using the proprietary code FracMan (Golder, 2005) and exporting the DFN output

into ELFEN.

7.1.3 Modelling Input Parameters

One of the key aspects in the numerical modelling of rock engineering problems

is establishing representative rock mass material strength and deformability

characteristics. As part of the current study the properties output from rock mass

classification systems were critically examined by comparison of RMR, GSI and

Q based properties for a fictitious dry, hard rock mass. In summary, comparison

of strength and deformability properties derived from the studied systems for

corresponding rating values for the most part showed a lack of consistency (see

Fig. 4.3 and 4.4). Generally, none of the studied rock mass classification based

correlations offered adequate estimates of all of the required equivalent

continuum rock mass properties. Output from these classifications should

undergo critical evaluation before being accepted in any analysis.

A novel block caving subsidence modelling methodology was devised and the

applicability of the use of RMR and Q rock mass classification systems as a

source of equivalent continuum properties for integrated FEM/DEM-DFN

modelling was analyzed. A series of numerical experiments were carried out to

investigate the behaviour of a system comprised of key discontinuities and an

equivalent continuum rock mass derived using varying assumptions for

mechanical properties from rock mass classification systems. A novel properties

assessment/calibration procedure that incorporates use of response constraining

criteria based on Laubscher‟s caveability chart (Diering & Laubscher, 1987), the

cave propagation concept of Duplancic & Brady (1999) and caving subsidence

experience was utilized.

The following are the key conclusions from the comparative analysis performed:

neither the RMR nor Q rock mass classification systems can be relied

upon as a robust source of rock mass properties for hybrid FEM/DEM

modelling;

220

very low estimates of rock mass cohesion and tensile strength derived

using RMR system led to overestimated susceptibility of simulated rock

mass material to tensile failure, making use of RMR properties

unacceptable for modelling of caving mechanisms;

among all considered Q property sets, the properties for the midrange Q

ratings, provide the most realistic representation of rock mass caveability,

cave development progression and subsidence response;

it appears that Q properties for the ratings equivalent to RMR 60 to 70

offer generally adequate estimates of deformation modulus, cohesion and

friction, and, also, give flexibility in regards to the assumption of the tensile

strength, thus leaving room for response calibration.

7.1.4 Factors Governing Block Caving Subsidence Development

In a complex block caving mining environment subsidence development is a

result of interplay of several governing factors. Mining experience suggests that

among such factors are geological structure (jointing and faults), rock mass

strength, in-situ stress level, mining depth, volume of extracted material and

varying lithological domains. A survey of the literature has shown that

publications are limited to a general, qualitative rather than quantitative,

description of the influence of geological structures on the observed subsidence.

Such qualitative observations are useful for initial subsidence analysis, however

they require further validation. With regards to other factors, literature sources

highlight their importance but provide only limited further description.

Understandably, discerning the effect of individual factors from field observations

is challenging. Adopting the novel modelling methodology for subsidence

analysis, through more than 30 extensive conceptual numerical experiments,

subsidence development mechanisms and the relative significance of the factors

governing subsidence were investigated.

The adopted modelling methodology allowed simulation of the subsidence

deformation mechanism, from caving initiation to the final subsidence, agreeing

closely with the observations based conceptual model of subsidence

221

development proposed by Abel & Lee (1980). This reinforced the validity of the

adopted approach for block caving subsidence analysis.

New valuable insights were gained into the complex mechanism of caving

induced rock mass deformations and subsequent subsidence development.

Conducted analyses clearly demonstrated the importance of joint set orientation

and persistence, and fault location and inclination, in determining the subsidence

development mechanisms and their governing role in defining the degree of

surface subsidence asymmetry. The modelling results correlated reasonably

well with the available field observations. Based on the analysis of conceptual

modelling study results a preliminary classification of block caving induced

surface subsidence for cases, where no major geological discontinuities intersect

the cave, is proposed, as shown in Table 5.8. This classification is

supplemented by a preliminary classification of the influence of major geological

discontinuities on surface subsidence, given in Table 5.9. The relative

significance of individual parameters is summarized in the influence assessment

matrix, shown in Table 5.10. The proposed subsidence assessment

classifications and the parametric influence matrix are meant to aid practical

engineering assessment of potential block caving subsidence at pre-feasibility

and design stages, and represent an important step towards better

understanding and quantifying block caving induced surface subsidence. It

cannot be over-emphasized that such assessments must be tailored to, and take

full consideration of, specific mine site conditions and should be based on sound

engineering judgement.

7.1.5 Large Open Pit - Block Caving Interaction

Brittle fracturing processes are one of the primary controls on slope deformation

development in large open pits. The FEM/DEM modelling approach was utilized

in the analysis of primary fracture process (using terminology of Stead et al.,

2007) associated with block caving induced step-path failure development in

large open pit slopes. The proposed “total interaction” analysis allowed relating

the destressing of the crown pillar due to caving to the development of unloading-

222

induced failure within the slope and the resultant subsidence at the surface.

Analysis indicated that there is a threshold or critical intact rock bridge

percentage along step-path failure planes that may ensure stability of an open pit

throughout caving operations.

Transition from open pit to underground mining at Palabora mine presents an

important example of the pit wall instability triggered by caving operation. Using

a combined FEM/DEM-DFN modelling approach it was possible to investigate

the formation of the basal failure surface within an open pit slope as a direct

result of caving. The modelling of Palabora highlighted the importance of rock

mass tensile strength and its influence on caving induced slope response.

7.2 Key Scientific Contributions

The following are the key contributions of this study:

A new FEM/DEM-DFN modelling approach was developed and

successfully applied to block caving subsidence and caving - large open

pit interaction analysis. This methodology allows physically realistic

simulation of the entire caving process from caving initiation to final

subsidence deformations.

Limitations of the rock mass classifications properties output were

highlighted and a procedure for calibrating rock mass classifications based

properties for FEM/DEM-DFN subsidence analysis was devised.

Through a comprehensive conceptual numerical modelling analysis major

advances were gained in our understanding of the general principles of

block caving induced subsidence development and the role of major

contributing factors. This included proposals for subsidence

characterization through an asymmetry index and the mobilized rock mass

volume. Based on the modelling results a preliminary quantitative

classification of block caving induced surface subsidence was proposed

and the role of major geological structures was classified. In addition, an

initial qualitative influence assessment matrix was proposed that

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summarizes the effect of major factors contributing to subsidence

development.

The principles of step-path failure development in large open-pit - caving

mining environment were investigated using a proposed “total interaction”

approach to modelling data interpretation. Indications of a critical rock

bridge percentage threshold in step-path failure development were found.

Applicability of the FEM/DEM-DFN modelling for practical engineering

analysis was demonstrated in the preliminary simulation of the Palabora

mine failure.

7.3 Recommendations for Further Research

7.3.1 Equivalent Continuum Rock Mass Properties

The analysis conducted clearly shows a need for further research into estimation

of rock mass equivalent continuum properties. In the author‟s opinion future

progress in this area can be achieved through use of a synthetic rock mass

modelling methodology employing either PFC or ELFEN and DFN techniques.

Further work is required to ensure that it can produce realistic material properties

for different rock mass scales and to evaluate its sensitivity to varying stochastic

realizations.

7.3.2 Modelling of 3D Aspects of Block Caving Subsidence Development

Current modelling was focused on 2D analysis. The actual rock mass conditions

however are three dimensional and more representative modelling should consider

3D effects. Of a particular interest are the 3D effects of rock mass fabric and 3D

slope stability in open-pit - block caving environment.

7.3.3 ELFEN Code Enhancements

The ELFEN code has shown strong capabilities to simulate highly complex rock

engineering problems. Further code improvements should make it more accessible

224

for practical engineering analysis. The following code improvements are

recommended:

I. ELFEN modelling carried out during present study demonstrated that the run-

times for simulations of caving induced deformations are often prohibitive for

practical engineering analysis. Adaptation of the code to support 64-bit and

parallel computing will allow affordable modelling of larger and more complex

problems in 2D and 3D space.

II. Another important improvement can be made in the inter-element fracturing

routine which is currently not robust (as discussed in Section 3.4.3), this

could allow consideration of coarser mesh further reducing simulations run-

time.

III. More realistic brittle fracture simulation can be achieved through

development of constitutive relationships that in addition to mode I support

mode II and mixed mode I-II fracturing in both 2D and 3D.

7.3.4 In-situ Subsidence Characterization

Literature reviews indicated very limited availability of factual (i.e. measured)

subsidence data at block cave mines. Such data is essential for constraining and

validating modelling studies. It is prudent to summarize the available information

from the current block caving mines and carry out a comprehensive subsidence

monitoring study using a combination of InSAR, LiDAR and photogrammetric

techniques, as well as traditional surveying methods and geotechnical

instrumentation at several block caving mines. Some elements of this work are

already being undertaken at SFU and UBC and it is hoped that the collected data

will further reinforce the validity of the modelling findings.

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APPENDIX A. PRELIMINARY STATISTICAL SUMMARY OF CONCEPTUAL STUDY MODELLING RESULTS

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

175 200 225 250 275 300 325 350 375 400 425

Pro

bab

ilit

y

Extent of major (≥10cm) vertical displacements, m

Fig. A.1 Probability (relative frequency) of the caving induced total extent of major (≥10cm) vertical surface displacements based on 37 model runs.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

175 200 225 250 275 300 325 350 375 400 425 450

Pro

bab

ilit

y

Extent of major (≥10cm) horizontal displacements, m

Fig. A.2 Probability of the caving induced total extent of major (≥10cm) horizontal surface displacements.

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0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

250 275 300 325 350 375 400 425 450 475 500 525 550 575 600

Pro

bab

ilit

y

Mobilized rock mass volume normalized by extracted ore volume, %

Fig. A.3 Probability of rock mass volume mobilized by caving, in percent of extracted ore

volume.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

45 50 55 60 65 70 75 80

Pro

bab

ilit

y

Minimum angles delineating the extent of major (≥10cm) surface displacements, degrees

Fig. A.4 Probability of minimum angles delineating the extent of caving induced major surface displacements.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.65 0.7 0.75 0.8 0.85 0.9 0.95 1

Pro

bab

ilit

y

Assymetry Index

Fig. A.5 Probability of subsidence asymmetry index.

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APPENDIX B. DFN PARAMETERS FOR PALABORA MODEL

Table B.1 Description of rock units present in the North Wall

Geological domain Joint Set Dip

direction / dip,◦ Fracture Intensity,

P10 Fracture length,

m

Carbonatite 160/07 0.1 10

130/90 0.1 10

Foskorite

160/07 0.06 10

020/85 0.03 10

225/85 0.03 10

Micaceous Pyroxenite

160/07 0.05 10

020/80 0.025 15

225/80 0.025 15

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APPENDIX C. DEVELOPMENT OF NORTH WALL FAILURE AT PALABORA MINE (PHOTOS)

Photographs presented in this Appendix are a courtesy of Rio Tinto Ltd and are

adapted with permission

Fig. C.1 Bench failure at the bottom of the pit - July 2004.

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Fig. C.2 Developing failure of the North Wall - October 7th, 2004.

Fig. C.3 Failed North Wall – late May, 2005.

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